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Articles 1 - 30 of 39
Full-Text Articles in Physical Sciences and Mathematics
Low Mach Number Fluctuating Hydrodynamics Of Diffusively Mixing Fluids, Aleksandar Donev, Andy J. Nonaka, Yifei Sun, Thomas Fai, Alejandro Garcia, John B. Bell
Low Mach Number Fluctuating Hydrodynamics Of Diffusively Mixing Fluids, Aleksandar Donev, Andy J. Nonaka, Yifei Sun, Thomas Fai, Alejandro Garcia, John B. Bell
Alejandro Garcia
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fast isentropic fluctuations in pressure associated with the propagation of sound waves by replacing the equation of state with a local thermodynamic constraint. We demonstrate that the low Mach number model preserves the spatio-temporal spectrum of the slower diffusive fluctuations. We develop a strictly conservative finite-volume spatial discretization of the low Mach number fluctuating equations in both two and three dimensions. We construct several explicit Runge-Kutta temporal integrators that strictly maintain the …
Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Ehsan Khatami
We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the …
Magnetic Correlations And Pairing In The 1/5-Depleted Square Lattice Hubbard Model, Ehsan Khatami, Rajiv R.P. Singh, Warren E. Pickett, Richard T. Scalettar
Magnetic Correlations And Pairing In The 1/5-Depleted Square Lattice Hubbard Model, Ehsan Khatami, Rajiv R.P. Singh, Warren E. Pickett, Richard T. Scalettar
Ehsan Khatami
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel phase. …
Finite-Temperature Properties Of Strongly Correlated Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marchos Rigol
Finite-Temperature Properties Of Strongly Correlated Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marchos Rigol
Ehsan Khatami
We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic …
Students Talk About Energy In Project- Based Inquiry Science, Benedikt W. Harrer, Virginia J. Flood, Michael C. Wittmann
Students Talk About Energy In Project- Based Inquiry Science, Benedikt W. Harrer, Virginia J. Flood, Michael C. Wittmann
Benedikt W. Harrer
We examine the types of emergent language eighth grade students in rural Maine middle schools use when they discuss energy in their first experiences with Project-Based Inquiry Science: Energy, a research-based curriculum that uses a specific language for talking about energy. By comparative analysis of the language used by the curriculum materials to students’ language, we find that students’ talk is at times more aligned with a Stores and Transfer model of energy than the Forms model supported by the curriculum.
Fluctuation-Dissipation Theorem In An Isolated System Of Quantum Dipolar Bosons After A Quench, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Fluctuation-Dissipation Theorem In An Isolated System Of Quantum Dipolar Bosons After A Quench, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Ehsan Khatami
We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find indications that fluctuation-dissipation relations hold if the system is nonintegrable after the quench, as well as if it is integrable after the quench if the initial state is an equilibrium state of a nonintegrable Hamiltonian. On the other hand, we find indications that they fail if the system is integrable both before and after quenching.
Productive Resources In Students’ Ideas About Energy: An Alternative Analysis Of Watts’ Original Interview Transcripts, Benedikt W. Harrer, Virginia J. Flood, Michael C. Wittmann
Productive Resources In Students’ Ideas About Energy: An Alternative Analysis Of Watts’ Original Interview Transcripts, Benedikt W. Harrer, Virginia J. Flood, Michael C. Wittmann
Benedikt W. Harrer
For over 30 years, researchers have investigated students’ ideas about energy with the intent of reforming instructional practice. In this pursuit, Watts contributed an influential study with his 1983 paper “Some alternative views of energy” [Phys. Educ. 18, 213 (1983)]. Watts’ “alternative frameworks” continue to be used for categorizing students’ non-normative ideas about energy. Using a resources framework, we propose an alternate analysis of student responses from Watts’ interviews. In our analysis, we show how students’ activated resources about energy are disciplinarily productive. We suggest that fostering seeds of scientific understandings in students’ ideas about energy may play an important …
Elements Of Proximal Formative Assessment In Learners’ Discourse About Energy, Benedikt W. Harrer, Rachel E. Scherr, Michael C. Wittmann, Hunter G. Close, Brian W. Frank
Elements Of Proximal Formative Assessment In Learners’ Discourse About Energy, Benedikt W. Harrer, Rachel E. Scherr, Michael C. Wittmann, Hunter G. Close, Brian W. Frank
Benedikt W. Harrer
Proximal formative assessment, the just-in-time elicitation of students' ideas that informs ongoing instruction, is usually associated with the instructor in a formal classroom setting. However, the elicitation, assessment, and subsequent instruction that characterize proximal formative assessment are also seen in discourse among peers. We present a case in which secondary teachers in a professional development course at SPU are discussing energy flow in refrigerators. In this episode, a peer is invited to share her thinking (elicitation). Her idea that refrigerators move heat from a relatively cold compartment to a hotter environment is inappropriately judged as incorrect (assessment). The "instruction" (peer …
Diffusive Transport Enhanced By Thermal Velocity Fluctuations, Alejandro Garcia, Aleksandar Donev, Anton De La Fuente, John B. Bell
Diffusive Transport Enhanced By Thermal Velocity Fluctuations, Alejandro Garcia, Aleksandar Donev, Anton De La Fuente, John B. Bell
Alejandro Garcia
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L0) in quasi-two-dimensional systems, while in three dimensions it scales as L0-1-L-1, where L0 is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.
Computational Fluctuating Fluid Dynamics, Alejandro Garcia, John B. Bell, Sarah Williams
Computational Fluctuating Fluid Dynamics, Alejandro Garcia, John B. Bell, Sarah Williams
Alejandro Garcia
This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret effect). We present various numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate good agreement with theoretical results and molecular simulation
On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell
On The Accuracy Of Explicit Finite-Volume Schemes For Fluctuating Hydrodynamics, Aleksandar Donev, Eric Vanden-Eijnden, Alejandro Garcia, John B. Bell
Alejandro Garcia
This paper describes the development and analysis of finite-volume methods for the Landau–Lifshitz Navier–Stokes (LLNS) equations and related stochastic partial differential equations in fluid dynamics. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by the addition of white noise fluxes whose magnitudes are set by a fluctuation-dissipation relation. Originally derived for equilibrium fluctuations, the LLNS equations have also been shown to be accurate for nonequilibrium systems. Previous studies of numerical methods for the LLNS equations focused primarily on measuring variances and correlations computed at equilibrium and for selected nonequilibrium flows. In this paper, we introduce a more systematic approach …
A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, Aleksandar Donev, John B. Bell, Berni Alder
A Hybrid Particle-Continuum Method For Hydrodynamics Of Complex Fluids, Alejandro Garcia, Aleksandar Donev, John B. Bell, Berni Alder
Alejandro Garcia
A previously developed hybrid particle-continuum method [J. B. Bell, A. Garcia, and S. A. Williams, Multiscale Model. Simul., 6 (2008), pp. 1256–1280] is generalized to dense fluids and two- and three-dimensional flows. The scheme couples an explicit fluctuating compressible Navier–Stokes solver with the isotropic direct simulation Monte Carlo (DSMC) particle method [A. Donev, A. L. Garcia, and B. J. Alder, J. Stat. Mech. Theory Exp., 2009 (2009), article P11008]. To achieve bidirectional dynamic coupling between the particle (microscale) and continuum (macroscale) regions, the continuum solver provides state-based boundary conditions to the particle subdomain, while the particle solver provides flux-based boundary …
Stochastic Hard-Sphere Dynamics For Hydrodynamics Of Non-Ideal Fluids, Alejandro Garcia, Aleksandar Donev, Berni J. Alder
Stochastic Hard-Sphere Dynamics For Hydrodynamics Of Non-Ideal Fluids, Alejandro Garcia, Aleksandar Donev, Berni J. Alder
Alejandro Garcia
A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Algorithm Refinement For Fluctuating Hydrodynamics, Alejandro Garcia, Sarah Williams, John B. Bell
Alejandro Garcia
This paper introduces an adaptive mesh and algorithm refinement method for fluctuating hydrodynamics. This particle-continuum hybrid simulates the dynamics of a compressible fluid with thermal fluctuations. The particle algorithm is direct simulation Monte Carlo (DSMC), a molecular-level scheme based on the Boltzmann equation. The continuum algorithm is based on the Landau–Lifshitz Navier–Stokes (LLNS) equations, which incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. It uses a recently developed solver for the LLNS equations based on third-order Runge–Kutta. We present numerical tests of systems in and out of equilibrium, including time-dependent systems, and demonstrate dynamic adaptive refinement by the …
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, John B. Bell, Sarah Williams
Numerical Methods For The Stochastic Landau-Lifshitz Navier-Stokes Equations, Alejandro Garcia, John B. Bell, Sarah Williams
Alejandro Garcia
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack’s two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk …
Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia
Estimating Hydrodynamic Quantities In The Presence Of Microscopic Fluctuations, Alejandro Garcia
Alejandro Garcia
This paper discusses the evaluation of hydrodynamic variables in the presence of spontaneous fluctuations, such as in molecular simulations of fluid flows. The principal point is that hydrodynamic variables such as fluid velocity and temperature must be defined in terms of mechanical variables such as momentum and energy density). Because these relations are nonlinear and because fluctuations of mechanical variables are correlated, care must be taken to avoid introducing a bias when evaluating means, variances, and correlations of hydrodynamic variables. The unbiased estimates are formulated; some alternative, incorrect approaches are presented as cautionary warnings. The expressions are verified by numerical …
Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, Malek M. Mansour
Hydrodynamic Description Of The Adiabatic Piston, Alejandro Garcia, Malek M. Mansour
Alejandro Garcia
A closed macroscopic equation for the motion of the two-dimensional adiabatic piston is derived from standard hydrodynamics. It predicts a damped oscillatory motion of the piston towards a final rest position, which depends on the initial state. In the limit of large piston mass, the solution of this equation is in quantitative agreement with the results obtained from both hard disk molecular dynamics and hydrodynamics. The explicit forms of the basic characteristics of the piston’s dynamics, such as the period of oscillations and the relaxation time, are derived. The limitations of the theory’s validity, in terms of the main system …
Rectification Of Thermal Fluctuations In Ideal Gases, Alejandro Garcia, P. Meurs, C. Van De Broeck
Rectification Of Thermal Fluctuations In Ideal Gases, Alejandro Garcia, P. Meurs, C. Van De Broeck
Alejandro Garcia
We calculate the systematic average speed of the adiabatic piston and a thermal Brownian motor, introduced by C. Van den Broeck, R. Kawai and P. Meurs [Phys. Rev. Lett. 93, 090601 (2004)], by an expansion of the Boltzmann equation and compare with the exact numerical solution.
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, Wolfgang Wagner
A Direct Simulation Monte Carlo Method For The Uehling-Uhlenbeck-Boltzmann Equation, Alejandro Garcia, Wolfgang Wagner
Alejandro Garcia
In this paper we describe a direct simulation Monte Carlo algorithm for the Uehling-Uhlenbeck-Boltzmann equation in terms of Markov processes. This provides a unifying framework for both the classical Boltzmann case as well as the Fermi-Dirac and Bose-Einstein cases. We establish the foundation of the algorithm by demonstrating its link to the kinetic equation. By numerical experiments we study its sensitivity to the number of simulation particles and to the discretization of the velocity space, when approximating the steady-state distribution.
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Inverted Velocity Profile In The Cylindrical Couette Flow Of A Rarefied Gas, Alejandro Garcia, K. Aoki, H. Yoshida, T. Nakanishi
Alejandro Garcia
The cylindrical Couette flow of a rarefied gas is investigated, under the diffuse-specular reflection condition of Maxwell’s type on the cylinders, in the case where the inner cylinder is rotating whereas the outer cylinder is at rest. The inverted velocity profile for small accommodation coefficients, pointed out by Tibbs, Baras, and Garcia [Phys. Rev. E 56, 2282 (1997)] on the basis of a Monte Carlo simulation, is investigated extensively by means of a systematic asymptotic analysis for small Knudsen numbers as well as the direct numerical analysis of the Boltzmann equation, and the parameter range in which the phenomenon appears …
Comment On ‘‘Stress-Density Ratio Slip-Corrected Reynolds Equation For Ultra-Thin Film Gas Bearing Lubrication’’, Alejandro Garcia
Comment On ‘‘Stress-Density Ratio Slip-Corrected Reynolds Equation For Ultra-Thin Film Gas Bearing Lubrication’’, Alejandro Garcia
Alejandro Garcia
No abstract provided.
Molecular Simulations Of Sound Wave Propagation In Simple Gases, Alejandro Garcia, N. Hadjiconstantinou
Molecular Simulations Of Sound Wave Propagation In Simple Gases, Alejandro Garcia, N. Hadjiconstantinou
Alejandro Garcia
Molecular simulations of sound waves propagating in a dilute hard sphere gas have been performed using the direct simulation Monte Carlo method. A wide range of frequencies is investigated, including very high frequencies for which the period is much shorter than the mean collision time. The simulation results are compared to experimental data and approximate solutions of the Boltzmann equation. It is shown that free molecular flow is important at distances smaller than one mean free path from the excitation point.
Time Step Truncation Error In Direct Simulation Monte Carlo, Alejandro Garcia, W. Wagner
Time Step Truncation Error In Direct Simulation Monte Carlo, Alejandro Garcia, W. Wagner
Alejandro Garcia
No abstract provided.
Erratum: "Cell Size Dependence Of Transport Coefficients In Stochastic Particle Algorithms", Alejandro Garcia, Francis Alexander, Berni Alder
Erratum: "Cell Size Dependence Of Transport Coefficients In Stochastic Particle Algorithms", Alejandro Garcia, Francis Alexander, Berni Alder
Alejandro Garcia
No abstract provided.
Burnett Description For Plane Poiseuille Flow, Alejandro Garcia, F. Uribe
Burnett Description For Plane Poiseuille Flow, Alejandro Garcia, F. Uribe
Alejandro Garcia
Two recent works have shown that at small Knudsen number ~K! the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. Malek-Mansour, Baras, and Garcia [Physica A 240, 255 (1997)] qualitatively confirmed these predictions in computer experiments using the direct simulation Monte Carlo method (DSMC). In this paper we compare the DSMC measurements of hydrodynamic variables and non-equilibrium fluxes with numerical …
Cell Size Dependence Of Transport Coefficients In Stochastic Particle Algorithms, Alejandro Garcia, F. Alexander, B. Alder
Cell Size Dependence Of Transport Coefficients In Stochastic Particle Algorithms, Alejandro Garcia, F. Alexander, B. Alder
Alejandro Garcia
Using the Green–Kubo theory, the dependence of the viscosity and thermal conductivity on cell size is obtained explicitly for stochastic particle methods such as direct simulation Monte Carlo (DSMC) and its generalization, the consistent Boltzmann algorithm (CBA). These analytical results confirm empirical observations that significant errors occur when the cell dimensions are larger than a mean free path.
Three-Dimensional Direct Simulation Monte Carlo Method For Slider Air Bearings, Alejandro Garcia, W. Huang, D. B. Bogy
Three-Dimensional Direct Simulation Monte Carlo Method For Slider Air Bearings, Alejandro Garcia, W. Huang, D. B. Bogy
Alejandro Garcia
The direct simulation Monte Carlo (DSMC) method is used to solve the three-dimensional nano-scale gas film lubrication problem between a gas bearing slider and a rotating disk, and this solution is compared to the numerical solution of the compressible Reynolds equations with the slip flow correction based on the linearized Boltzmann equation as presented by Fukui and Kaneko [molecular gas film lubrication (MGL) method] [ASME J. Tribol. 110, 253 (1988)]. In the DSMC method, hundreds of thousands of simulated particles are used and their three velocity components and three spatial coordinates are calculated and recorded by using a hard-sphere collision …
Anomalous Flow Profile Due To The Curvature Effect On Slip Length, Alejandro Garcia, K. Tibbs, F. Baras
Anomalous Flow Profile Due To The Curvature Effect On Slip Length, Alejandro Garcia, K. Tibbs, F. Baras
Alejandro Garcia
No abstract provided.
A Simple Model For Nonequilibrium Fluctuations In A Fluid, Alejandro Garcia, F. Baras, M. Malek Mansour
A Simple Model For Nonequilibrium Fluctuations In A Fluid, Alejandro Garcia, F. Baras, M. Malek Mansour
Alejandro Garcia
Presents a train model that shows the long-range spatial correlations of fluctuations in nonequilibrium fluid systems. Illustration of model through analysis of flat-car trains running on parallel tracks; Simulation of train model in computers; Theoretical analysis for fluctuations in the train model; Relationship between train model and the fluctuating hydrodynamic theory of fluids.
Comment On 'Simulation Of A Two-Dimensional Rayleigh-Bénard System Using The Direct Simulation Monte Carlo Method, Alejandro Garcia, F. Baras, M. Malek Mansour
Comment On 'Simulation Of A Two-Dimensional Rayleigh-Bénard System Using The Direct Simulation Monte Carlo Method, Alejandro Garcia, F. Baras, M. Malek Mansour
Alejandro Garcia
No abstract provided.