2024-03-29T11:40:29Z
http://docs.lib.purdue.edu/do/oai/
oai:docs.lib.purdue.edu:nanodocs-1183
2010-10-12T17:49:53Z
publication:dp
publication:prism
publication:nanodocs
publication:nano
A domain adaptive stochastic collocation approach for analysis of MEMS under uncertainties
Agarwal, Nitin
Aluru, N R
Article
This work proposes a domain adaptive stochastic collocation approach for uncertainty quantification, suitable for effective handling of discontinuities or sharp variations in the random domain. The basic idea of the proposed methodology is to adaptively decompose the random domain into subdomains. Within each subdomain, a sparse grid interpolant is constructed using the classical Smolyak construction [S. Smolyak, Quadrature and interpo- lation formulas for tensor products of certain classes of functions, Soviet Math. Dokl. 4 (1963) 240–243], to approximate the stochastic solution locally. The adaptive strategy is governed by the hierarchical surpluses, which are computed as part of the interpolation procedure. These hierarchical surpluses then serve as an error indicator for each subdo- main, and lead to subdivision whenever it becomes greater than a threshold value. The hierarchical surpluses also provide information about the more important dimensions, and accordingly the random elements can be split along those dimensions. The proposed adaptive approach is employed to quantify the effect of uncertainty in input parameters on the performance of micro-electromechanical systems (MEMS). Specifically, we study the effect of uncertain material properties and geometrical parameters on the pull-in behavior and actuation properties of a MEMS switch. Using the adaptive approach, we resolve the pull-in instability in MEMS switches. The results from the proposed approach are verified using Monte Carlo simulations and it is demonstrated that it computes the required statistics effectively.
Multiphysics; Stochastic collocation; Stochastic Galerkin method; Sparse grids; Adaptive sampling; Reliability; Geometrical uncertainty; Uncertainty propagation
Nanoscience and Nanotechnology
2009-11-01T07:00:00Z
https://docs.lib.purdue.edu/nanodocs/175
oai:docs.lib.purdue.edu:prism-1001
2010-10-14T18:18:46Z
publication:dp
publication:prism
publication:nano
Vertical Carbon Nanotube Devices With Nanoscale Lengths Controlled Without Lithography
Franklin, Aaron D.
Sayer, Robert A.
Sands, Timothy D.
Janes, David B.
Fisher, Timothy S.
Article
IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 8, NO. 4, JULY 2009. © 2009 IEEE. doi:10.1109/TNANO.2009.2012399
Vertical single-walled carbon nanotubes (vSWCNTs) are synthesized within highly ordered porous anodic alumina (PAA) templates supported on Si substrates. A process for obtaining thin-film PAA with long-range ordered nanopores is presented in this paper. Each nanopore contains at most one v-SWCNT that is supported by a dielectric and addressed by electrochemically formed Pd nanowire source contacts and evaporated Pd drain contacts. Characteristics of these completely vertical, two-terminal nanotube devices are presented. Control of the v-SWCNT length is demonstrated using a straightforward etching process with lengths of less than 100 nm achieved without the need for complex/expensive lithography. This effective nanoscale length control of highly ordered v-SWCNTs provides a practical basis for the realization of CNT-based nanoelectronics.
Field-Effect Transistors
High-Performance Electronics
Aligned Arrays
Fabrication
Templates
Contacts
FETS
Carbon nanotubes (CNTs)
length scaling
nanotechnology
porous anodic alumina (PAA)
vertical devices
Nanoscience and Nanotechnology
2009-07-01T07:00:00Z
https://docs.lib.purdue.edu/prism/1
oai:docs.lib.purdue.edu:prism-1000
2010-10-14T18:02:06Z
publication:dp
publication:prism
publication:nano
Unified Theory Of Gas Damping Of Flexible Microcantilevers At Low Ambient Pressures
Bidkar, Rahul
Tung, Ryan
Alexeenko, Alina
Hartono, Sumali
Raman, Arvind
Article
© 2009 American Institute of Physics
doi:10.1063/1.3122933
Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.
Boltzmann equation; cantilevers; damping; elemental semiconductors; Knudsen flow; microfluidics; microsensors; silicon; slip flow
Engineering
Nanoscience and Nanotechnology
2009-04-20T07:00:00Z
https://docs.lib.purdue.edu/prism/2
oai:docs.lib.purdue.edu:prism-1002
2010-10-14T18:46:48Z
publication:dp
publication:prism
publication:nano
Structures And Energetics Of Silicon Nanotubes From Molecular Dynamics And Density Functional Theory
Palaria, Amritanshu
Klimeck, Gerhard
Strachan, Alejandro
Article
©2008 The American Physical Society. doi:10.1103/PhysRevB.78.205315
We use molecular dynamics with a first-principles-based force field and density functional theory to predict the atomic structure, energetics, and elastic properties of Si nanotubes. We find various low-energy and low-symmetry hollow structures with external diameters of about 1 nm. These are the most stable structures in this small-diameter regime reported so far and exhibit properties very different from the bulk. While the cohesive energies of the four most stable nanotubes reported here are similar (from 0.638 to 0.697 eV above bulk Si), they have disparate Young's moduli (from 72 to 123 GPa).
Nanowires
Performance
Field
Engineering
Nanoscience and Nanotechnology
2008-11-01T07:00:00Z
https://docs.lib.purdue.edu/prism/4
oai:docs.lib.purdue.edu:prism-1003
2012-07-09T17:42:28Z
publication:dp
publication:prism
publication:nano
Weighted Matrix Ordering And Parallel Banded Preconditioners For Iterative Linear System Solvers
Manguoglu, Murat
Koyuturk, Mehmet
Sameh, Ahmed
Grama, Ananth Y.
Article
<p>© 2010 Society for Industrial and Applied Mathematics. doi:10.1137/080713409</p>
<p>The emergence of multicore architectures and highly scalable platforms motivates the development of novel algorithms and techniques that emphasize concurrency and are tolerant of deep memory hierarchies, as opposed to minimizing raw FLOP counts. While direct solvers are reliable, they are often slow and memory-intensive for large problems. Iterative solvers, on the other hand, are more efficient but, in the absence of robust preconditioners, lack reliability. While preconditioners based on incomplete factorizations ( whenever they exist) are effective for many problems, their parallel scalability is generally limited. In this paper, we advocate the use of banded preconditioners instead and introduce a reordering strategy that enables their extraction. In contrast to traditional bandwidth reduction techniques, our reordering strategy takes into account the magnitude of the matrix entries, bringing the heaviest elements closer to the diagonal, thus enabling the use of banded preconditioners. When used with effective banded solvers-in our case, the Spike solver-we show that banded preconditioners (i) are more robust compared to the broad class of incomplete factorization-based preconditioners, (ii) deliver higher processor performance, resulting in faster time to solution, and (iii) scale to larger parallel configurations. We demonstrate these results experimentally on a large class of problems selected from diverse application domains.</p>
Permuting Large Entries
Sparse Matrices
Algorithm
Indefinite
Scheme
Graphs
Computation
Reduction
Flows
Spike
spectral reordering
weighted reordering
banded preconditioner
incomplete factorization
Krylov subspace methods
parallel preconditioners
Engineering
Nanoscience and Nanotechnology
2010-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/3
oai:docs.lib.purdue.edu:prism-1004
2010-10-19T13:22:22Z
publication:dp
publication:prism
publication:nano
Stochastic Analysis of Electrostatic MEMS Subjected to Parameter Variations
Agarwal, Nitin
Aluru, Narayana R.
Article
© 2009 IEEE. doi:10.1109/JMEMS.2009.2034612
This paper presents an efficient stochastic framework for quantifying the effect of stochastic variations in various design parameters such as material properties, geometrical features, and/or operating conditions on the performance of electrostatic microelectromechanical systems (MEMS) devices. The stochastic framework treats uncertainty as a separate dimension, in addition to space and time, and seeks to approximate the stochastic dependent variables using sparse grid interpolation in the multidimensional random space. This approach can be effectively used to compute important information, such as moments (mean and variance), failure probabilities, and sensitivities with respect to design variables, regarding relevant quantities of interest. The approach is straightforward to implement and, depending on the accuracy required, can be orders of magnitude faster than the traditional Monte Carlo method. We consider two examples-MEMS switch and resonator-and employ the proposed approach to study the effect of uncertain Young's modulus and various geometrical parameters, such as dimensions of electrodes and gap between microstructures, on relevant quantities of interest such as actuation behavior, resonant frequency, and quality factor. It is demonstrated that, in addition to computing the required statistics and probability density function, the proposed approach effectively identifies critical design parameters, which can then be controlled during fabrication, in order to improve device performance and reliability.
Differential-Equations
Design Optimization
Lagrangian Approach
Dynamic-Analysis
Actuated MEMS
Robust
Uncertainty
Resonators
Simulation
Schemes
Microelectromechanical systems (MEMS) resonator
MEMS switch
parameter variation
reliability
Smolyak algorithm
sparse grid interpolation
uncertainty propagation
Nanoscience and Nanotechnology
2009-12-01T08:00:00Z
https://docs.lib.purdue.edu/prism/14
oai:docs.lib.purdue.edu:prism-1006
2010-10-20T15:42:05Z
publication:dp
publication:prism
publication:nano
PuReMD Manual (Purdue Reactive Molecular Dynamics Program)
Aktulga, Hasan Metin
Article
Nanoscience and Nanotechnology
2010-06-06T07:00:00Z
https://docs.lib.purdue.edu/prism/12
oai:docs.lib.purdue.edu:prism-1007
2012-07-09T17:38:52Z
publication:dp
publication:prism
publication:nano
A Reactive Molecular Dynamics Simulation Of The Silica-Water Interface
Fogarty, Joseph C.
Aktulga, Hasan Metin
Grama, Ananth Y.
Van Duin, Adri C. T.
Pandit, Sagar A.
Article
<p>© 2010 American Institute of Physics. doi:10.1063/1.3407433</p>
<p>We report our study of a silica-water interface using reactive molecular dynamics. This first-of-its-kind simulation achieves length and time scales required to investigate the detailed chemistry of the system. Our molecular dynamics approach is based on the ReaxFF force field of van Duin [J. Phys. Chem. A 107, 3803 (2003)]. The specific ReaxFF implementation (SERIALREAX) and force fields are first validated on structural properties of pure silica and water systems. Chemical reactions between reactive water and dangling bonds on a freshly cut silica surface are analyzed by studying changing chemical composition at the interface. In our simulations, reactions involving silanol groups reach chemical equilibrium in similar to 250 ps. It is observed that water molecules penetrate a silica film through a proton-transfer process we call "hydrogen hopping," which is similar to the Grotthuss mechanism. In this process, hydrogen atoms pass through the film by associating and dissociating with oxygen atoms within bulk silica, as opposed to diffusion of intact water molecules. The effective diffusion constant for this process, taken to be that of hydrogen atoms within silica, is calculated to be 1.68x10(-6) cm(2)/s. Polarization of water molecules in proximity of the silica surface is also observed. The subsequent alignment of dipoles leads to an electric potential difference of similar to 10.5 V between the silica slab and water.</p>
Amorphous Silica
Vitreous Silica
Force-Field
Charge Equilibration
Dipole-Moment
Liquid Water
Surface
Nanoparticles
Spectroscopy
Diffusion
association
chemical equilibrium
chemical exchanges
dangling bonds
dissociation
interface structure
molecular dynamics method
polarisation
silicon compounds
surface diffusion
water
Nanoscience and Nanotechnology
2010-05-07T07:00:00Z
https://docs.lib.purdue.edu/prism/11
oai:docs.lib.purdue.edu:prism-1009
2010-10-20T17:26:33Z
publication:dp
publication:prism
publication:nano
Numerical Simulation Of Gas-Phonon Coupling In Thermal Transpiration Flows
Guo, Xiaohui
Singh, Dhruv
Murthy, Jayathi
Alexeenko, Alina A.
Article
©2009 The American Physical Society. doi:10.1103/PhysRevE.80.046310
Thermal transpiration is a rarefied gas flow driven by a wall temperature gradient and is a promising mechanism for gas pumping without moving parts, known as the Knudsen pump. Obtaining temperature measurements along capillary walls in a Knudsen pump is difficult due to extremely small length scales. Meanwhile, simplified analytical models are not applicable under the practical operating conditions of a thermal transpiration device, where the gas flow is in the transitional rarefied regime. Here, we present a coupled gas-phonon heat transfer and flow model to study a closed thermal transpiration system. Discretized Boltzmann equations are solved for molecular transport in the gas phase and phonon transport in the solid. The wall temperature distribution is the direct result of the interfacial coupling based on mass conservation and energy balance at gas-solid interfaces and is not specified a priori unlike in the previous modeling efforts. Capillary length scales of the order of phonon mean free path result in a smaller temperature gradient along the transpiration channel as compared to that predicted by the continuum solid-phase heat transfer. The effects of governing parameters such as thermal gradients, capillary geometry, gas and phonon Knudsen numbers and, gas-surface interaction parameters on the efficiency of thermal transpiration are investigated in light of the coupled model.
Knudsen Compressor
Boltzmann-Equation
Prandtl Number
heat-transfer
rarefied-gas
conductivity
performance
transport
MEMS
Boltzmann equation
capillarity
channel flow
flow simulation
heat transfer
Knudsen flow
phonons
rarefied fluid dynamics
sorption
transpiration
Nanoscience and Nanotechnology
2009-10-01T07:00:00Z
https://docs.lib.purdue.edu/prism/9
oai:docs.lib.purdue.edu:prism-1008
2010-10-20T17:18:23Z
publication:dp
publication:prism
publication:nano
Toward Surround Gates On Vertical Single-Walled Carbon Nanotube Devices
Franklin, Aaron D.
Sayer, Robert A.
Sands, Timothy D.
Fisher, Timothy S.
Janes, David B.
Article
©2009 American Vacuum Society. doi:10.1116/1.3054266
The one-dimensional, cylindrical nature of single-walled carbon nanotubes (SWCNTs) suggests that the ideal gating geometry for nanotube field-effect transistors (FETs) is a surround gate (SG). Using vertical SWCNTs templated in porous anodic alumina, SGs are formed using top-down processes for the dielectric/metal depositions and definition of the channel length. Surround gates allow aggressive scaling of the channel to 25% of the length attainable with a bottom-gate geometry without incurring short-channel effects. The process demonstrated here for forming SGs on vertical SWCNTs is amenable for large-scale fabrication of multinanotube FETs.
field-effect transistor
high-performance electronics
porous alumina
arrays
lithography
fabrication
templates
circuits
contact
silicon
Nanoscience and Nanotechnology
2009-03-01T08:00:00Z
https://docs.lib.purdue.edu/prism/10
oai:docs.lib.purdue.edu:prism-1011
2010-10-20T17:41:58Z
publication:dp
publication:prism
publication:nano
A Numerical Fatigue Damage Model for Life Scatter of MEMS Devices
Jalalahmadi, Behrooz
Sadeghi, Farshid
Peroulis, Dimitrios
Article
© 2009 IEEE. doi:10.1109/JMEMS.2009.2024800
This paper presents a fatigue damage model to estimate fatigue lives of microelectromechanical systems (MEMS) devices and account for the effects of topological randomness of material microstructure. For this purpose, the damage mechanics modeling approach is incorporated into a new Voronoi finite-element model (VFEM). The VFEM developed for this investigation is able to consider both intergranular crack initiation (debonding) and propagation stages. The model relates the fatigue life to a damage parameter "D" which is a measure of the gradual material degradation under cyclic loading. The fatigue damage model is then used to investigate the effects of microstructure randomness on the fatigue of MEMS. In this paper, three different types of randomness are considered: 1) randomness in the microstructure due to random shapes and sizes of the material grains; 2) the randomness in the material properties considering a normally (Gaussian) distributed elastic modulus; and 3) the randomness in the material properties considering a normally distributed resistance stress, which is the experimentally determined material property controlling the ability of a material to resist the damage accumulation. Thirty-one numerical models of MEMS specimens are considered under cyclic axial and bending loading conditions. It is observed that the stress-life results obtained are in good agreement with the experimental study. The effects of material inhomogeneity and internal voids are numerically investigated.
high-cycle fatigue
polycrystalline silicon
thin-films
liga ni
mechanical-properties
fracture-behavior
specimen size
microstructures
strength
failure
damage mechanics
fatigue behavior
material microstructure
microelectromechanical systems (MEMS) devices
numerical simulation
Nanoscience and Nanotechnology
2009-10-01T07:00:00Z
https://docs.lib.purdue.edu/prism/7
oai:docs.lib.purdue.edu:prism-1013
2012-07-10T16:30:08Z
publication:dp
publication:prism
publication:nano
Strain Relaxation In Si/Ge/Si Nanoscale Bars From Molecular Dynamics Simulations
Park, Yumi
Atkulga, Hasan Metin
Grama, Ananth Y.
Strachan, Alejandro
Article
<p>We use molecular dynamics (MD) with the reactive interatomic potential ReaxFF to characterize the local strains of epitaxial Si/Ge/Si nanoscale bars as a function of their width and height. While the longitudinal strain (along the bars length) is independent of geometry, surface relaxation leads to transverse strain relaxation in the Ge section. This strain relaxation increases with increasing height of the Ge section and reduction in its width and is complete (i.e., zero transverse strain) for roughly square cross sections of Ge leading to a uniaxial strain state. Such strain state is desirable in some microelectronics applications. From the MD results, which are in excellent agreement with experiments, we derive a simple model to predict lateral strain as a function of geometry for this class of nanobars.</p>
field-effect transistors
reactive force-field
p-type
silicon
heterostructures
potentials
insulator
shear
elemental semiconductors
germanium
molecular dynamics method
nanostructured materials
potential energy functions
semiconductor heterojunctions
silicon
stress relaxation
Nanoscience and Nanotechnology
2009-08-01T07:00:00Z
https://docs.lib.purdue.edu/prism/5
oai:docs.lib.purdue.edu:prism-1012
2010-10-20T17:46:17Z
publication:dp
publication:prism
publication:nano
Nanoscale Metal-Metal Contact Physics from Molecular Dynamics: The Strongest Contact Size
Kim, Hojin
Strachan, Alejandro
Article
© 2010 The American Physical Society. doi:10.1103/PhysRevLett.104.215504
Using molecular dynamics we find that the tensile strength of the contacts between two clean platinum surfaces with nanoscale asperities is strongly size dependent with a maximum strength for contact lengths of approximately 5 nm. This is the first time a strongest size is observed in single crystals. The strengthening with decreasing size down to 5 nm results from a decrease in the initial density of mobile dislocations available for plastic deformation and the subsequent weakening originates from a reduction in the constraint to mechanical deformation inside the contact by the bulk.
nanocrystalline metals
crystal plasticity
deformation
strength
copper
Nanoscience and Nanotechnology
2010-05-28T07:00:00Z
https://docs.lib.purdue.edu/prism/6
oai:docs.lib.purdue.edu:nanopub-1597
2019-06-21T14:19:52Z
publication:dp
publication:engr
publication:prism
publication:nanopub
publication:nano
publication:ece
publication:ecepubs
Shot Noise Thermometry for Thermal Characterization of Templated Carbon Nanotubes
Sayer, Robert A
Kim, Sunkook
Franklin, Aaron D
Mohammadi, Saeed
Fisher, Timothy
<p>A carbon nanotube (CNT) thermometer that operates on the principles of electrical shot noise is reported. Shot noise thermometry is a self-calibrating measurement technique that relates statistical fluctuations in dc current across a device to temperature. A structure consisting of vertical, top, and bottom-contacted single-walled carbon nanotubes in a porous anodic alumina template was fabricated and used to measure shot noise. Frequencies between 60 and 100 kHz were observed to preclude significant influence from 1/f noise, which does not contain thermally relevant information. Because isothermal models do not accurately reproduce the observed noise trends, a self-heating shot noise model has been developed and applied to experimental data to determine the thermal resistance of a CNT device consisting of an array of vertical single-walled CNTs supported in a porous anodic alumina template. The thermal surface resistance at the nanotube-dielectric interface is found to be 1.5 x 10(8) K/W, which is consistent with measurements by other techniques.</p>
Carbon nanotubes; electrical noise; thermal resistance
2010-03-01T08:00:00Z
Article
Engineering
Nanoscience and Nanotechnology
https://docs.lib.purdue.edu/nanopub/608
oai:docs.lib.purdue.edu:prism-1014
2010-10-21T19:26:26Z
publication:dp
publication:prism
publication:nano
Comprehensive Reduced-Order Models Of Electrostatically Actuated MEMS Switches And Their Dynamics Including Impact And Bounce
Snow, Michael G.
Bajaj, Anil K.
Article
Proceedings of the ASME 2010 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference
IDETC/CIE 2010 August 15-18, 2010, Montreal, Quebec, Canada. Copyright © 2010 by ASME
As MEMS technology develops it is becoming better understood that MEMS designers must account for the large uncertainties characteristic of the relevant manufacturing processes. Uncertainty quantification tasks the designer with evaluating many different possible outcomes from the manufacturing process which creates a demand for models that are accurate and comprehensive, yet fast to evaluate. This work presents a comprehensive reduced-order model of electrostatically actuated switches incorporating a range of effects that are typically included only in FE modeling codes. Specifically, the model accounts for variable electrode geometry, stretching of centerline or large displacement effects, fringing field, squeeze film and rarefied gas damping, and allows for elastic contact with the dielectric substrate. Individual compact models for each of these effects are taken from literature and included in the model for the system. The dielectric substrate is modeled as an elastic foundation. The resulting partial differential equation for the switch modeled as a beam is discritized via a Galerkin method into ordinary differential equations for modal amplitudes. The Galerkin method uses the linear un-damped mode shapes of the beam to approximate the solution. Both cantilever and fixed-fixed type switches are analyzed. Static equilibrium solutions as a function of the applied voltage are developed along with their stability. Static pull-in voltages, first time of switch closure, and voltage for lift-off are studied with the model. To capture the contact dynamics, the contact condition is evaluated with the substrate divided into a large number of elements and the contact force is projected on to the beam basis functions. In the case of cantilever geometry and slow voltage variations, three stable regimes of contact configuration and hysteresis between them are demonstrated.
Nanoscience and Nanotechnology
2010-08-15T07:00:00Z
https://docs.lib.purdue.edu/prism/21
oai:docs.lib.purdue.edu:prism-1017
2012-07-09T17:44:50Z
publication:dp
publication:prism
publication:nano
Parallel Reactive Molecular Dynamics: Numerical Methods and Algorithmic Techniques
Aktulga, Hasan Metin
Fogarty, Joseph C.
Pandit, Sagar A.
Grama, Ananth Y
Article
Nanoscience and Nanotechnology
2009-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/18
oai:docs.lib.purdue.edu:prism-1019
2010-10-21T19:52:23Z
publication:dp
publication:prism
publication:nano
A Stochastic Collocation Approach to Bayesian Inference in Inverse Problems
Marzouk, Youssef
Xiu, Dongbin
Article
© 2009 Global-Science Press
We present an efficient numerical strategy for the Bayesian solution of inverse problems. Stochastic collocation methods, based on generalized polynomial chaos (gPC), are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. This approximation then defines a surrogate posterior probability density that can be evaluated repeatedly at minimal computational cost. The ability to simulate a large number of samples from the posterior distribution results in very accurate estimates of the inverse solution and its associated uncertainty. Combined with high accuracy of the gPC-based forward solver, the new algorithm can provide great efficiency in practical applications. A rigorous error analysis of the algorithm is conducted, where we establish convergence of the approximate posterior to the true posterior and obtain an estimate of the convergence rate. It is proved that fast (exponential) convergence of the gPC forward solution yields similarly fast (exponential) convergence of the posterior. The numerical strategy and the predicted convergence rates are then demonstrated on nonlinear inverse problems ofvarying smoothness and dimension.
Inverse problems
Bayesian inference
stochastic collocation
generalized polynomial
Nanoscience and Nanotechnology
2009-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/16
oai:docs.lib.purdue.edu:prism-1020
2010-10-21T19:58:48Z
publication:dp
publication:prism
publication:nano
Compact Model Of Squeeze-Film Damping Based On Rarefied Flow Simulations
Guo, Xiaohui
Alexeenko, Alina
Article
© 2009 IOP Publishing Ltd. doi:10.1088/0960-1317/19/4/045026
A new compact model of squeeze-film damping is developed based on the numerical solution of the Boltzmann kinetic equation. It provides a simple expression for the damping coefficient and the quality factor valid through the slip, transitional and free-molecular regimes. In this work, we have applied statistical analysis to the current model using the chi-squared test. The damping predictions are compared with both Reynolds equation-based models and experimental data. At high Knudsen numbers, the structural damping dominates the gas squeeze-film damping. When the structural damping is subtracted from the measured total damping force, good agreement is found between the model predictions and the experimental data.
Nanoscience and Nanotechnology
2009-04-01T07:00:00Z
https://docs.lib.purdue.edu/prism/15
oai:docs.lib.purdue.edu:prism-1018
2010-10-21T19:49:24Z
publication:dp
publication:prism
publication:nano
A Generalized Polynomial Chaos Based Ensemble Kalman Filter
Li, Jia
Xiu, Dongbin
Article
© 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2009.04.029
As one of the most adopted sequential data assimilation methods in many areas, especially those involving complex nonlinear dynamics, the ensemble Kalman filter (EnKF) has been under extensive investigation regarding its properties and efficiency. Compared to other variants of the Kalman filter (KF), EnKF is straightforward to implement, as it employs random ensembles to represent solution states. This, however, introduces sampling errors that affect the accuracy of EnKF in a negative manner. Though sampling errors can be easily reduced by using a large number of samples, in practice this is undesirable as each ensemble member is a solution of the system of state equations and can be time consuming to compute for large-scale problems. In this paper we present an efficient EnKF implementation via generalized polynomial chaos (gPC) expansion. The key ingredients of the proposed approach involve (1) solving the system of stochastic state equations via the gPC methodology to gain efficiency; and (2) sampling the gPC approximation of the stochastic solution with an arbitrarily large number of samples, at virtually no additional computational cost, to drastically reduce the sampling errors. The resulting algorithm thus achieves a high accuracy at reduced computational cost, compared to the classical implementations of EnKF. Numerical examples are provided to verify the convergence property and accuracy improvement of the new algorithm. We also prove that for linear systems with Gaussian noise, the first-order gPC Kalman filter method is equivalent to the exact Kalman filter.
Kalman filter
data assimilation
polynomial chaos
uncertainty quantification
Nanoscience and Nanotechnology
2009-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/17
oai:docs.lib.purdue.edu:prism-1015
2010-10-21T19:32:12Z
publication:dp
publication:prism
publication:nano
Uncertainty Quantification Study For A Comprehensive Electrostatic MEMS Switch Model
Snow, Michael G.
Bajaj, Anil K.
Article
This work presents an uncertainty analysis of a comprehensive model for an electrostatic MEMS switch. The goal is to elucidate the effects of parameter variations on certain performance characteristics. A sufficiently detailed model of an electrostatically actuated beam is developed. This model accounts for various physical effects, including the electrostatic fringing field, finite length of electrodes, squeeze film damping, and contact between the beam and the dielectric layer. The performance characteristics of immediate interest are the static and dynamic pull-in voltages for switch. Using Latin Hypercube and other sampling methods, the model is evaluated to find these performances characteristics when variability in the model’s geometric and physical parameters is specified. Response surfaces of these results were constructed via Multivariate Adaptive Regression Splines (MARS). Using a Direct Simulation Monte Carlo (DSMC) technique on these response surfaces gives smooth PDF’s of the outputs. The relative variation in output due to each input is used to determine the critical parameters.
Nanoscience and Nanotechnology
2010-09-20T07:00:00Z
https://docs.lib.purdue.edu/prism/20
oai:docs.lib.purdue.edu:prism-1022
2010-11-01T19:13:21Z
publication:dp
publication:prism
publication:nano
Modeling Of Subcontinuum Thermal Transport Across Semiconductor-Gas Interfaces
Singh, Dhruv
Guo, Xiaohui
Alexeenko, Alina
Murthy, Jayathi Y.
Fisher, Timothy S.
Article
© 2009 American Institute of Physics. doi: 10.1063/1.3181059
A physically rigorous computational algorithm is developed and applied to calculate subcontinuum thermal transport in structures containing semiconductor-gas interfaces. The solution is based on a finite volume discretization of the Boltzmann equation for gas molecules in the gas phase and phonons in the semiconductor. A partial equilibrium is assumed between gas molecules and phonons at the interface of the two media, and the degree of this equilibrium is determined by the accommodation coefficients of gas molecules and phonons on either side of the interface. Energy balance is imposed to obtain a value of the interface temperature. The classic problem of temperature drop across a solid-gas interface is investigated with a simultaneous treatment of solid and gas phase properties for the first time. A range of transport regimes is studied, varying from ballistic phonon transport and free molecular flow to continuum heat transfer in both gas and solid. A reduced-order model is developed that captures the thermal resistance of the gas-solid interface. The formulation is then applied to the problem of combined gas-solid heat transfer in a two-dimensional nanoporous bed and the overall thermal resistance of the bed is characterize in terms of the governing parameters. These two examples exemplify the broad utility of the model in practical nanoscale heat transfer applications.
Nanoscience and Nanotechnology
2009-07-31T07:00:00Z
https://docs.lib.purdue.edu/prism/30
oai:docs.lib.purdue.edu:prism-1021
2010-11-01T18:55:31Z
publication:dp
publication:prism
publication:nano
A Continuum Plasticity Model That Accounts For Hardening And Size Effects In Thin Films
Hunter, Abigail
Kavuri, Hariharanath
Koslowski, Marisol
Article
We conducted three-dimensional finite element simulations of the mechanical
response of passivated single crystal copper thin films with a continuum
crystal plasticity model. The model introduces the formation of high density
dislocation layers close to the substrate and passivation interfaces obtained from
dislocation dynamics simulations. These dislocation structures are responsible
for an increase in strain hardening as the film thickness decreases. The model
predicts an increase in strain hardening as the film thickness decreases in
agreement with experimental observation in films with thickness in the range
0.2 to 2μm.
Nanoscience and Nanotechnology
2010-03-01T08:00:00Z
https://docs.lib.purdue.edu/prism/31
oai:docs.lib.purdue.edu:prism-1023
2010-11-01T19:18:58Z
publication:dp
publication:prism
publication:nano
Uncertainty Quantification Models For Micro-Scale Squeeze-Film Damping
Guo, Xiaohui
Li, Jia
Xiu, Dongbin
Alexeenko, Alina
Article
Copyright © 2010 John Wiley & Sons, Ltd. doi:10.1002/nme.2952
Two squeeze-film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro-electro-mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro-structures, knowledge of parameter dependence in gas damping contributes to the understanding of device-level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non-parametric distributions. A good agreement has been found, within 1%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes.
uncertainty quantification; squeeze-film damping; gPC expansion; rarefied flow
Nanoscience and Nanotechnology
2010-04-01T07:00:00Z
https://docs.lib.purdue.edu/prism/29
oai:docs.lib.purdue.edu:prism-1025
2010-11-01T19:31:32Z
publication:dp
publication:prism
publication:nano
Squeeze-Film Damping Of Flexible Microcantilevers At Low Ambient Pressures: Theory And Experiment
Lee, Jin Woo
Tung, Ryan
Raman, Arvind
Sumali, Hartono
Sullivan, John
Article
© 2009 IOP Publishing Ltd. doi:10.1088/0960-1317/19/10/105029
An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems.
Nanoscience and Nanotechnology
2009-09-24T07:00:00Z
https://docs.lib.purdue.edu/prism/27
oai:docs.lib.purdue.edu:prism-1026
2010-11-01T19:37:34Z
publication:dp
publication:prism
publication:nano
Unusual Scaling Obsrvations in the Quality Factors of Cantilevered Carbon Nanotube Resonators
Vallabhaneni, Ajit K.
Rhoads, Jeffrey F.
Ruan, Xiulin
Murthy, Jayathi Y.
Article
Proceedings of the ASME 2010 International Mechanical Engineering Congress & Exposition IMECE2010 November 12-18, 2010, Vancouver, British Columbia, Canada.
This work examines the quality factors (Q factors) of resonance associated with the axial and transverse vibrations of single-wall carbon nanotube (SWCNT) resonators through the use of molecular dynamics (MD) simulation. Specifically, the work investigates the effect of device length, diameter, and chirality, as well as temperature, on the resonant frequency and quality factor of these devices, and benchmarks the results of MD simulation against classical theories of energy dissipation. Of note are the facts that the quality factors associated with transverse vibration decrease with increasing device diameter and are largely insensitive to chirality. Additionally, quality factors increase with increasing device length for transverse vibrations, but remain almost constant for axial vibrations. The predicted size dependence of the quality factors associated with axial vibration agrees well with classical theory, if the nanoscale size effect of thermal conductivity is properly accounted for. However, the size dependence of the quality factors associated with transverse vibrations deviates significantly from classical theory.
Nanoscience and Nanotechnology
2010-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/26
oai:docs.lib.purdue.edu:prism-1028
2010-11-01T19:44:48Z
publication:dp
publication:prism
publication:nano
What Determines Knudsen Force At The Microscale
Nabeth, Jeremy S.
Chigullapalli, Sruti
Alexeenko, Alina A.
Article
Knudsen forces arise in microscale systems when there is a thermal gradient with a characteristic length scale comparable to the molecular mean free path of the ambient gas. These forces are sometimes referred as radiometric or thermo-molecular forces [1] and have been recently measured experimentally in a microscale configuration using heated atomic force microscopy (AFM) probes [2]. The Knudsen force on microstructures with thermal gradients can provide a novel actuation mechanism for mass detection, thermogravimetry, and very high-resolution heat flux measurements. While measuring such forces precisely at microscale can be an arduous task especially since only limited analytical results exist, numerical simulations can provide a basis for understanding the physical mechanisms governing the generation of Knudsen forces. The main goal of this paper is to determine the dependence of the Knudsen force on pressure, geometry and thermal gradients based on rarefied flow simulations and to investigate the effects of the Knudsen force on the dynamics of microbeams.
Nanoscience and Nanotechnology
2010-07-01T07:00:00Z
https://docs.lib.purdue.edu/prism/24
oai:docs.lib.purdue.edu:prism-1030
2012-07-09T17:40:29Z
publication:dp
publication:prism
publication:nano
Reactive Molecular Dynamics: Numerical Methods And Algorithmic Techniques
Aktulga, Hasan Metin
Pandit, Shailaja
van Duin, Adri C. T.
Grama, Ananth Y.
Article
<p>Modeling atomic and molecular systems requires computation-intensive quantum mechanical methods such as, but not limited to, density functional theory (DFT) [11]. These methods have been successful in predicting various properties of chemical systems at atomistic detail. Due to the inherent nonlocality of quantum mechanics, the scalability of these methods ranges from O(N3) to O(N7) depending on the method used and approximations involved. This significantly limits the size of simulated systems to a few thousands of atoms, even on large scale parallel platforms. On the other hand, classical approximations of quantum systems, although computationally (relatively) easy to implement, yield simpler models that lack essential chemical properties such as reactivity and charge transfer. The recent work of van Duin et al [9] overcomes the limitations of classical molecular dynamics approximations by carefully incorporating limited nonlocality (to mimic quantum behavior) through empirical bond order potential. This reactive molecular dynamics method, called ReaxFF, achieves essential quantum properties, while retaining computational simplicity of classical molecular dynamics, to a large extent. Implementation of reactive force fields presents significant algorithmic challenges. Since these methods model bond breaking and formation, efficient implementations must rely on complex dynamic data structures. Charge transfer in these methods is accomplished by minimizing electrostatic energy through charge equilibriation. This requires the solution of large linear systems (108 degrees of freedom and beyond) with shielded electrostatic kernels at each timestep. Individual timesteps are themselves typically in the range of tenths of femtoseconds, requiring optimizations within and across timesteps to scale simulations to nanoseconds and beyond, where interesting phenomena may be observed. In this paper, we present implementation details of sPuReMD (serial Purdue Reactive Molecular Dynamics) program, a unique reactive molecular dynamics code. We describe various data structures, and the charge equilibration solver at the core of the simulation engine. This Krylov subspace solver relies on an ILU-based preconditioner, specially targeted to our application. We comprehensively validate the performance and accuracy of sPuReMD on a variety of hydrocarbon systems. In particular, we show excellent per-timestep time, linear time scaling in system size, and a low memory footprint. sPuReMD is available over the public domain and is currently being used to model diverse</p>
Reactive Molecular Dynamics
Bond Order Potentials
ReaxFF
Charge Equilibration.
Nanoscience and Nanotechnology
2010-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/22
oai:docs.lib.purdue.edu:prism-1027
2010-11-01T19:41:42Z
publication:dp
publication:prism
publication:nano
Knudsen Force Modeling in Application to Microsystems
Nabeth, Jeremy S.
Chigullapalli, Sruti
Alexeenko, Alina A.
Article
10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 28 Jun - 1 Jul 2010 , Chicago, Illinois
At the microscale, even moderate temperature differences can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Creating, controlling and measuring Knudsen forces in microsystems can be an arduous task since only limited theory exists at present. This present study investigates the mechanism of Knudsen forces in detail based on numerical solution of the Boltzmann kinetic equation. The Knudsen force is shown, in general, to be a result of thermal nonequilibrium between gas and solid. The simulations are validated by comparison with experimental measurements that have been reported by Passian et al.10 using heated atomic force microscope probes. A closed-form model for the Knudsen force on a beam is obtained based on the simulations and can be applied for analysis and design of microsystems.
Nanoscience and Nanotechnology
2010-07-01T07:00:00Z
https://docs.lib.purdue.edu/prism/25
oai:docs.lib.purdue.edu:prism-1031
2010-11-04T18:38:52Z
publication:dp
publication:prism
publication:nano
Real-Time Monitoring Of Contact Behaviour Of RF MEMS Switches With A Very Low Power CMOS Capactive Sensor Interface
Fruehling, Adam
Khater, Mohammad Abu
Jung, Byunghoo
Peroulis, Dimitrios
Article
© 2010 IEEE
This paper presents the first ultra-low power, fully electronic methodology for real-time monitoring of the dynamic behavior of RF MEMS switches. The measurement is based on a capacitive readout circuit composed of 67 transistors with 105 µm x 105 µm footprint consuming as little as 60 µW. This is achieved by accurately sensing the capacitance change around the contact region at sampling rates from 10 kHz to 5 MHz. Experimental and simulation results show that times of not only the first contact event but also all subsequent contact bounces can be accurately measured with this technique without interfering with the switch performance. This demonstrates the potential of extending this technique to real-time on-chip dynamic monitoring of packaged RF MEMS switches through their entire lifetime and after their integration in their final system.
Nanoscience and Nanotechnology
2010-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/32
oai:docs.lib.purdue.edu:prism-1033
2010-11-04T18:52:09Z
publication:dp
publication:prism
publication:nano
Entropy Considerations In Numerical Simulations Of Non-Equilibrium Rarefied Flows
Chigullapalli, Sruti
Venkattraman, A.
Ivanov, M. S.
Alexeenko, Alina A.
Article
Non-equilibrium rarefied flows are encountered frequently in supersonic flight at high altitudes, vacuum technology and in microscale devices. Prediction of the onset of non-equilibrium is important for accurate numerical simulation of such flows. We formulate and apply the discrete version of Boltzmann’s H-theorem for analysis of non-equilibrium onset and accuracy of numerical modeling of rarefied gas flows. The numerical modeling approach is based on the deterministic solution of kinetic model equations. The numerical solution approach comprises the discrete velocity method in the velocity space and the finite volume method in the physical space with different numerical flux schemes: the first-order, the second-order minmod flux limiter and a third-order WENO schemes. The use of entropy considerations in rarefied flow simulations is illustrated for the normal shock, the Riemann and the two-dimensional shock tube problems. The entropy generation rate based on kinetic theory is shown to be a powerful indicator of the onset of non-equilibrium, accuracy of numerical solution as well as the compatibility of boundary conditions for both steady and unsteady problems.
Rarefied gas flows; Kinetic theory; Non-continuum effects; Numerical methods; Shock waves
Nanoscience and Nanotechnology
2009-11-26T08:00:00Z
https://docs.lib.purdue.edu/prism/35
oai:docs.lib.purdue.edu:prism-1034
2010-11-04T18:58:29Z
publication:dp
publication:prism
publication:nano
A Parallel Spectral Element Method For Dynamic Three-Dimensional Nonlinear Elasticity Problems
Dong, S.
Yosibash, Z.
Article
We present a high-order method employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics, for solving dynamic three-dimensional geometrically nonlinear elasticity problems. We demonstrate that the method has an exponential convergence rate spatially and a second-order accuracy temporally for the four classes of problems of linear/geometrically nonlinear elastostatics/elastodynamics. The method is parallelized through domain decomposition and message passing interface (MPI), and is scaled to over 2000 processors with high parallel performance.
Spectral element method; hp finite element method; Exponential convergence; Jacobi polynomial; Nonlinear elasticity; Message passing interface
Nanoscience and Nanotechnology
2008-09-25T07:00:00Z
https://docs.lib.purdue.edu/prism/34
oai:docs.lib.purdue.edu:prism-1035
2010-11-04T19:02:11Z
publication:dp
publication:prism
publication:nano
BDF-Like Methods For Nonlinear Dynamic Analysis
Dong, S.
Article
http://dx.doi.org/10.1016/j.jcp.2009.12.028
We present several time integration algorithms of second-order accuracy that are numerically simple and effective for nonlinear elastodynamic problems. These algorithms are based on a general four-step scheme that has a resemblance to the backward differentiation formulas. We also present an extension to the composite strategy of the Bathe method. Appropriate values for the algorithmic parameters are determined based on considerations of stability and dissipativity, and less dissipative members of each algorithm have been identified. We demonstrate the convergence characteristics of the proposed algorithms with a nonlinear dynamic problem having analytic solutions, and test these algorithms with several three-dimensional nonlinear elastodynamic problems involving large deformations and rotations, employing St. Venant-Kirchhoff and compressible Neo-Hookean hyperelastic material models. These tests show that stable computations are obtained with the proposed algorithms in nonlinear situations where the trapezoidal rule encounters a well-known instability.
Nonlinear dynamics; Time integration; Backward differentiation formula
Nanoscience and Nanotechnology
2010-01-04T08:00:00Z
https://docs.lib.purdue.edu/prism/33
oai:docs.lib.purdue.edu:prism-1036
2010-11-29T17:23:09Z
publication:dp
publication:prism
publication:nano
Coarse grain modeling of spall failure in molecular crystals: role of intra-molecular degrees of freedom
Lynch, Karen
Thompson, Alexander
Strachan, Alejandro
Article
We use a recently developed thermodynamically accurate mesodynamical method (Strachan and Holian 2005 Phys. Rev. Lett. 94 014301) where groups of atoms are represented by mesoparticles to characterize the shock compression and dynamical failure (spall) of a model molecular crystal. We characterize how the temperature rise caused by the shockwave depends on the specific heat of the degrees of freedom (DoFs) internal to the mesoparticles (Cint) and the strength of the coupling between the internal DoFs and the mesoparticles. We find that the temperature of the shocked material decreases with increasing Cint and decreasing coupling and quantify these effects. Our simulations also show that the threshold for plastic deformation (the Hugoniot elastic limit) depends on the properties of the internal DoFs while the threshold for failure is very insensitive to them. These results have implications on the results of all-atom MD simulations, whose classical nature leads to a significant overestimation of the specific heat of molecular materials.
Nanoscience and Nanotechnology
2009-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/38
oai:docs.lib.purdue.edu:prism-1037
2010-11-29T18:22:08Z
publication:dp
publication:prism
publication:nano
AN UNSTRUCTURED FINITE VOLUME METHOD FOR INCOMPRESSIBLE FLOWS WITH COMPLEX IMMERSED BOUNDARIES
Sun, Lin
Mathur, Sanjay
Murthy, Jayathi
Article
A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving solids of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flow is accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres and cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.
SIMULATING FLOWS; FLUID; DYNAMICS; MESHES; 3D
Nanoscience and Nanotechnology
2009-11-13T08:00:00Z
https://docs.lib.purdue.edu/prism/37
oai:docs.lib.purdue.edu:prism-1039
2010-11-30T14:42:03Z
publication:dp
publication:prism
publication:nano
SIMULATION OF SUB-MICRON THERMAL TRANSPORT IN A MOSFET USING A
Loy, James
Singh, Druv
Murthy, Jayathi Y
Article
Self-heating has emerged as a critical bottleneck to
scaling in modern transistors. In simulating heat conduction in
these devices, it is important to account for the granularity of
phonon transport since electron-phonon scattering occurs
preferentially to select phonon groups. However, a complete
accounting for phonon dispersion, polarization and scattering is
very expensive if the Boltzmann transport equation (BTE) is
used. Moreover, difficulties with convergence are encountered
when the phonon Knudsen number becomes small. In this
paper we simulate a two-dimensional bulk MOSFET hotspot
problem using a partially-implicit hybrid BTE-Fourier solver
which is significantly less expensive than a full BTE solution,
and which shows excellent convergence characteristics.
Volumetric heat generation from electron-phonon collisions is
taken from a Monte Carlo simulation of electron transport and
serves as a heat source term in the governing transport
equations. The hybrid solver is shown to perform well in this
highly non-equilibrium situation, matching the solutions
obtained from a pure all-BTE solution, but at significantly
lower computational cost. The paper establishes that this new
model and solution methodology are viable for the simulation
of thermal transport in other emerging transistor designs and in
other nanotechnology applications as well.
Nanoscience and Nanotechnology
2010-08-08T07:00:00Z
https://docs.lib.purdue.edu/prism/39
oai:docs.lib.purdue.edu:prism-1038
2010-11-30T14:36:21Z
publication:dp
publication:prism
publication:nano
NON-GRAY PHONON TRANSPORT USING A HYBRID BTE-FOURIER SOLVER
Loy, James
Singh, Druv
Murthy, Jayathi Y
Article
Non-gray phonon transport solvers based on the Boltzmann
transport equation (BTE) are frequently employed to simulate
sub-micron thermal transport. Typical solution procedures
using sequential solution schemes encounter numerical
difficulties because of the large spread in scattering rates. For
frequency bands with very low Knudsen numbers, strong
coupling between the directional BTEs results in slow
convergence for sequential solution procedures. In this paper,
we present a hybrid BTE-Fourier model which addresses this
issue. By establishing a phonon group cutoff (say Kn=0.1),
phonon bands with low Knudsen numbers are solved using a
modified Fourier equation which includes a scattering term as
well as corrections to account for boundary temperature slip.
Phonon bands with high Knudsen numbers are solved using a
BTE solver. Once the governing equations are solved for
each phonon group, their energies are then summed to find the
total lattice energy and correspondingly, the lattice
temperature. An iterative procedure combining the lattice
temperature determination and the solutions to the modified
Fourier and BTE equations is developed. The procedure is
shown to work well across a range of Knudsen numbers.
Nanoscience and Nanotechnology
2009-07-19T07:00:00Z
https://docs.lib.purdue.edu/prism/40
oai:docs.lib.purdue.edu:prism-1040
2010-11-30T18:18:50Z
publication:dp
publication:prism
publication:nano
Squeeze-film damping of flexible microcantilevers at low ambient pressures: theory and experiment
Lee, Jin
Tung, Ryan C
Raman, Arvind
Sumali, Hartono
Sullivan, John
Article
An improved theoretical approach is proposed to predict the dynamic behavior of long, slender
and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our
approach extends recent continuum gas damping models (Veijola 2004 J. Micromech.
Microeng. 14 1109–18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653–9),
which were originally derived for a rigid oscillating plate near a wall, to flexible
microcantilevers for calculating and predicting squeeze-film damping ratios of higher order
bending modes at reduced ambient pressures. Theoretical frequency response functions are
derived for a flexible microcantilever beam excited both inertially and via external forcing.
Experiments performed carefully at controlled gas pressures are used to validate our
theoretical approach over five orders of the Knudsen number. In addition, we investigate the
relative importance of theoretical assumptions made in the Reynolds-equation-based approach
for flexible microelectromechanical systems.
Nanoscience and Nanotechnology
2009-07-12T07:00:00Z
https://docs.lib.purdue.edu/prism/41
oai:docs.lib.purdue.edu:prism-1042
2010-12-02T18:55:34Z
publication:dp
publication:prism
publication:nano
An Experimental Investigation on Viscoelastic Behavior in Tunable
Hsu, Hao-Han
Peroulis, Dimitrios
Article
Abstract—In this paper, the viscoelastic behavior of a tunable
RF-MEMS resonator and its impacts are studied by means of
direct RF measurements for the first time. This tunable resonator
consists of one λ/2 coplanar waveguide (CPW) resonator and
two nanocrystalline-Ni RF-MEMS varactors. S-parameters of
this tunable resonator have been measured for 80 hours under
a bi-state bias condition of 0 and 40 V. It is demonstrated that
the resonant frequency is shifted by 90 MHz and the varactor
deformed by 0.12 μm over the 80 hour period. The gap of the
loaded varactor is extracted from the measured S-parameters
using finite-element analysis (FEA) tools. A generalized Voigt-
Kelvin model is employed to verify the viscoelastic behavior
of the resonator. The creep compliance extracted from the RF
measurements is in excellent agreement with results in literature.
Index Terms—creep, nickel, RF-MEMS, tunable resonator,
viscoelastic.
Nanoscience and Nanotechnology
2010-05-01T07:00:00Z
https://docs.lib.purdue.edu/prism/46
oai:docs.lib.purdue.edu:prism-1046
2010-12-02T19:24:58Z
publication:dp
publication:prism
publication:nano
Uncertainty propagation in a multiscale model of nanocrystalline plasticity
Koslowski, Marisol
Strachan, Alejandro
Article
We characterize how uncertainties propagate across spatial and temporal scales in a physicsbased
model of nanocrystalline plasticity of fcc metals. Our model combines molecular dynamics
(MD) simulations to characterize atomic level processes that govern dislocation basedplastic
deformation with a phase field approach to dislocation dynamics (PFDD) that describes
how an ensemble of dislocations evolve and interact to determine the mechanical response
of the material. We apply this approach to a nanocrystalline Ni specimen of interest in
micro-electromechanical (MEMS) switches. Our approach enables us to quantify how internal
stresses that result from the fabrication process affect the properties of dislocations (using MD)
and how these properties, in turn, affect the yield stress of the metallic membrane (using the
PFMM model). Our predictions show that, for a nanocrystalline sample with small grain size
(4 nm), a variation in residual stress of 20 MPa (typical in today’s microfabrication techniques)
would result in a variation on the critical resolved shear yield stress of approximately 15 MPa,
a very small fraction of the nominal value of approximately 9 GPa.
Nanoscience and Nanotechnology
2010-12-01T08:00:00Z
https://docs.lib.purdue.edu/prism/42
oai:docs.lib.purdue.edu:prism-1043
2010-12-02T19:14:43Z
publication:dp
publication:prism
publication:nano
An Unstructured Finite Volume Method For Incompressible Flows with Complex Immersed Boundaries
Sun, Lin
Mathur, Sanjay
Murthy, Jayathi Y
Article
A numerical method is developed for solving the 3D, unsteady, incompressible flows with immersed moving soldis of arbitrary geometrical complexity. A co-located (non-staggered) finite volume method is employed to solve the Navier-Stokes governing equeations for flow region using arbitrary convex polyhedral meshes. The solid region is represented by a set of material points with known position and velocity. Faces in the flow region located in the immediate vicinity of the solid body are marked as immersed boundary (IB) faces. At every instant in time, the influence of the body on the flowis accounted for by reconstructing implicitly the velocity the IB faces from a stencil of fluid cells and solid material points. Specific numerical issues related to the non-staggered formulation are addressed, including the specification of face mass fluxes, and corrections to the continuity equation to ensure overall mass balance. Incorporation of this immersed boundary technique within the framework of the SIMPLE algorithm is described. Canonical test cases of laminar flow around stationary and moving spheres adn cylinders are used to verify the implementation. Mesh convergence tests are carried out. The simulation results are shown to agree well with experiments for the case of micro-cantilevers vibrating in a viscous fluid.
Nanoscience and Nanotechnology
2009-11-13T08:00:00Z
https://docs.lib.purdue.edu/prism/45
oai:docs.lib.purdue.edu:prism-1045
2010-12-02T19:21:59Z
publication:dp
publication:prism
publication:nano
Thermal conduction in molecular materials using coarse grain dynamics: Role of mass diffusion and quantum corrections for molecular dynamics simulations
Zhou, Ya
Strachan, Alejandro
Article
We use a mesodynamical method, denoted dynamics with implicit degrees of freedom DID, to
characterize thermal transport in a model molecular crystal below and above its melting
temperature. DID represents groups of atoms molecules in this case using mesoparticles and the
thermal role of the intramolecular degrees of freedom DoFs are described implicitly using their
specific heat. We focus on the role of these intramolecular DoFs on thermal transport. We find that
thermal conductivity is independent of intramolecular specific heat for solid samples and a linear
relationship between the two quantities in liquid samples with the coefficient of proportionality
being the mass diffusivity of the mesoparticles. As the temperature of the liquids is increased,
thermal conductivity exhibits an increased sensitivity with respect to the specific heat of the internal
DoFs due to the enhanced molecular mobility. Based on these results, we propose a simple method
to incorporate quantum corrections to thermal conductivity obtained from nonequilibrium molecular
dynamics simulations of molecular liquids. Our results also provide insight into the development of
thermally accurate coarse grain models of soft materials.
Nanoscience and Nanotechnology
2009-12-21T08:00:00Z
https://docs.lib.purdue.edu/prism/43
oai:docs.lib.purdue.edu:prism-1044
2010-12-02T19:18:30Z
publication:dp
publication:prism
publication:nano
Phase stability and transformations in NiTi from density
Vishnu, Karthik Guda
Strachan, Alejandro
Article
We used density functional theory to characterize various crystalline phases of NiTi alloys: (i) high-temperature austenite phase B2;
(ii) orthorhombic B19; (iii) the monoclinic martensite phase B190; and (iv) a body-centered orthorhombic phase (BCO), theoretically predicted
to be the ground state. We also investigated possible transition pathways between the various phases and the energetics involved.
We found B19 to be metastable with a 1 meV energy barrier separating it from B190. Interestingly, we predicted a new phase of NiTi,
denoted B1900, that is involved in the transition between B190 and BCO. B1900 is monoclinic and can exhibit shape memory; furthermore,
its presence reduces the internal stress required to stabilize the experimentally observed B190 structure, and it consequently plays a key
role in NiTi’s properties.
NiTi; Martensitic phase transformation; Density functional theory (DFT); Shape memory alloys (SMA)
Nanoscience and Nanotechnology
2009-11-10T08:00:00Z
https://docs.lib.purdue.edu/prism/44
oai:docs.lib.purdue.edu:prism-1041
2010-12-02T18:52:35Z
publication:dp
publication:prism
publication:nano
A VISCOELASTIC-AWARE EXPERIMENTALLY-DERIVED MODEL FOR ANALOG RF MEMS VARACTORS
Hsu, Hao-Han
Peroulis, Dimitrios
Article
In this paper we present, for the ¯rst time, an
experimentally-extracted model for the spring con-
stant and tuning range of an analog RF-MEMS var-
actor that includes viscoelastic e®ects in RF-MEMS
devices. By utilizing a bi-state bias condition with
one state lasting 60 minutes and the other 1 minute,
this model focuses on capturing the true electrome-
chanical behavior of the varactor. An experimental
setup with very high long-term accuracy is created
to measure capacitance of the varactor up to 1,370
hours. The impact of these e®ects and the e®ective-
ness of the model are demonstrated on a tunable-
resonator loaded with RF-MEMS varactors.
Nanoscience and Nanotechnology
2010-01-01T08:00:00Z
https://docs.lib.purdue.edu/prism/47
oai:docs.lib.purdue.edu:prism-1047
2010-12-02T19:31:11Z
publication:dp
publication:prism
publication:nano
Strain rate sensitivity of nanocrystalline Au films at room temperature
Jonnalagadda, K
Karanjgaokar, N
Chee, Joo lien
Peroulis, Dimitrios
Article
The effect of strain rate on the inelastic properties of nanocrystalline Au films was quantified with 0.85 and 1.76 lm free-standing
microscale tension specimens tested over eight decades of strain rate, between 6 106 and 20 s1. The elastic modulus was independent
of the strain rate, 66 ± 4.5 GPa, but the inelastic mechanical response was clearly rate sensitive. The yield strength and the ultimate tensile
strength increased with the strain rate in the ranges 575–895 MPa and 675–940 MPa, respectively, with the yield strength reaching the
tensile strength at strain rates faster than 101 s1. The activation volumes for the two film thicknesses were 4.5 and 8.1 b3, at strain rates
smaller than 104 s1 and 12.5 and 14.6 b3 at strain rates higher than 104 s1, while the strain rate sensitivity factor and the ultimate
tensile strain increased below 104 s1. The latter trends indicated that the strain rate regime 105–104 s1 is pivotal in the mechanical
response of the particular nanocrystalline Au films. The increased rate sensitivity and the reduced activation volume at slow strain rates
were attributed to grain boundary processes that also led to prolonged (5–6 h) and significant primary creep with initial strain rate of the
order of 107 s1.
Nanocrystalline materials; Thin films; Ductility; Microvoids; Creep tests
Nanoscience and Nanotechnology
2010-06-03T07:00:00Z
https://docs.lib.purdue.edu/prism/48
oai:docs.lib.purdue.edu:prism-1048
2012-06-20T19:53:21Z
publication:dp
publication:prism
publication:nano
Numerical approach for quantification of epistemic uncertainty
Jakeman, John
Eldred, Michael
Xiu, Dongbin
Article
<p>In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty, little attention has been given to the quantification of epistemic uncertainty. In this paper, we propose a numerical framework for quantification of epistemic uncertainty. The proposed methodology does not require any probabilistic information on uncertain input parameters. The method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability. To quantify the epistemic uncertainty, we solve an encapsulation problem, which is a solution to the original governing equations defined on the estimated range of the input variables. We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty. In the case where probability distributions of the epistemic variables become known a posteriori, we can use the information to post-process the solution and evaluate solution statistics. Convergence results are also established for such cases, along with strategies for dealing with mixed aleatory and epistemic uncertainty. Several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology. (C) 2010 Elsevier Inc. All rights reserved.</p>
Uncertainty quantification; Epistemic uncertainty; Generalized polynomial chaos; Stochastic collocation; Encapsulation problem;STOCHASTIC DIFFERENTIAL-EQUATIONS; POLYNOMIAL CHAOS; PROPAGATION
Nanoscience and Nanotechnology
2010-06-20T07:00:00Z
https://docs.lib.purdue.edu/prism/49