The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of t...
The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. It is shown that the interaction of the random and large-scale coherent components of the Clebsch fields is responsible for generation of two energy spectra E(k)∝k−7/3 and E(k)∝k−2 at scales somewhat larger than those corresponding to the -5/3 inertial range. This interaction is also responsible for the experimentally observed Gaussian statistics of the velocity differences at large scales, and the nontrivial scaling behavior of their high-order moments for inertial-range values of the displacement r. The ‘‘anomalous scaling exponents’’ are derived and compared with experimental data.
We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various gen...
We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various generalizations of the classical Cauchy-Born rule. In particular, we discuss a so-called local Cauchy-Born rule which is very general and particularly easy to use. As an application, we use the atomistically derived continuum models to study the elastic deformation of carbon nanotubes.
This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the bo...
This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of α-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.
Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time poin...
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ISBN:
(纸本)160560352X
Functional Magnetic Resonance Imaging (fMRI) provides dynamical access into the complex functioning of the human brain, detailing the hemodynamic activity of thousands of voxels during hundreds of sequential time points. One approach towards illuminating the connection between fMRI and cognitive function is through decoding;how do the time series of voxel activities combine to provide information about internal and external experience? Here we seek models of fMRI decoding which are balanced between the simplicity of their interpretation and the effectiveness of their prediction. We use signals from a subject immersed in virtual reality to compare global and local methods of prediction applying both linear and nonlinear techniques of dimensionality reduction. We find that the prediction of complex stimuli is remarkably low-dimensional, saturating with less than 100 features. In particular, we build effective models based on the decorrelated components of cognitive activity in the classically-defined Brodmann areas. For some of the stimuli, the top predictive areas were surprisingly transparent, including Wernicke's area for verbal instructions, visual cortex for facial and body features, and visual-temporal regions for velocity. Direct sensory experience resulted in the most robust predictions, with the highest correlation (c ∼ 0:8) between the predicted and experienced time series of verbal instructions. Techniques based on non-linear dimensionality reduction (Laplacian eigenmaps) performed similarly. The interpretability and relative simplicity of our approach provides a conceptual basis upon which to build more sophisticated techniques for fMRI decoding and offers a window into cognitive function during dynamic, natural experience.
Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model f...
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Scaling properties of the field equation governing propagation of a thin flame front in a turbulent medium are discussed. It is shown that if the turbulent flame velocity uγcan be expressed through the turbulence int...
We explore time-based solvers for linear standing-wave problems, especially the oscillatory Helmholtz equation. Here, we show how to accelerate the convergence properties of timestepping. We introduce a new time-based...
We explore time-based solvers for linear standing-wave problems, especially the oscillatory Helmholtz equation. Here, we show how to accelerate the convergence properties of timestepping. We introduce a new time-based solver that we call phase-adjusted time-averaging (PATA), which we couple to timestepping to form the PATA-TS solver. Numerical experiments indicate that the PATA-TS solver is faster than the PATA solver and timestepping by a factor of 1.2 and 1.5 or more, respectively. We also explain why the PATA-TS solver is robust, efficient, and easy to program for a variety of practical applications.
The large-scale, long-time properties of a compressible fluid stirred by a Gaussian random force with correlation 〈fifj〉∝k−y are investigated. It is shown that when ε=4+y-d>3 (d=space dimension) the effective s...
The large-scale, long-time properties of a compressible fluid stirred by a Gaussian random force with correlation 〈fifj〉∝k−y are investigated. It is shown that when ε=4+y-d>3 (d=space dimension) the effective sound velocity becomes scale dependent in the limit k→0 and the fluid obeys a universal equation of state. The effective Mach number is also scale dependent, reaching a fixed-point value Ma*(k)<1 when k→0. The predictions of the theory are compared with the results of direct numerical simulations.
Let Dt and BΩ denote the operators which cut the time content outside T and the frequency content outside Ω, respectively. The prolate spheroidal functions are the eigen-functions of the operator Ρτ,Ω = DtBΩDt. ...
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It is shown that a gas composed of inelastically colliding particles is unstable to the formation of high density clusters. A possible physical mechanism underlying this instability is proposed. A theoretical analysis...
It is shown that a gas composed of inelastically colliding particles is unstable to the formation of high density clusters. A possible physical mechanism underlying this instability is proposed. A theoretical analysis, based on the Jenkins-Richman equations, as well as a numerical simulation of the dynamics of an unforced system of hard disks in a periodic rectangular enclosure, renders support to the proposed mechanism. In particular, a simple formula for the characteristic intercluster distance is derived and found to be in agreement with the numerical results. Applications to granular systems of engineering interest as well as to astrophysics are briefly outlined.
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