arXiv subjects

M. C. Cross

Publications and source records attributed to M. C. Cross.

At least 55 records · Page 3Linked to original sources

arXiv2002

Surface scattering analysis of phonon transport in the quantum limit using an elastic model

We have investigated the effect on phonon energy transport in mesoscopic systems and the reduction in the thermal conductance in the quantum limit due to phonon scattering by surface roughness using full 3-dimensional elasticity theory for an elastic beam with a rectangular cross-section. At low frequencies we find power laws for the scattering coefficients that are strongly mode dependent, and different from the $ω^{2}$ dependence, deriving from Rayleigh scattering of scalar waves, that is often assumed. The scattering gives contributions to the reduction in thermal conductance with the same power laws. At higher frequencies the scattering coefficients becomes large at the onset frequency of each mode due to the flat dispersion here. We use our results to attempt a quantitative understanding of the suppression of the thermal conductance from the universal value observed in experiment.

cond-mat.mes-hall↗

arXiv2001

The Effect of Surface Roughness on the Universal Thermal Conductance

We explain the reduction of the thermal conductance below the predicted universal value observed by Schwab et al. in terms of the scattering of thermal phonons off surface roughness using a scalar model for the elastic waves. Our analysis shows that the thermal conductance depends on two roughness parameters: the roughness amplitude $δ$ and the correlation length $a$. At sufficiently low temperatures the conductance decrease from the universal value quadratically with temperature at a rate proportional to $δ^{2}a$. Values of $δ$ equal to 0.22 and $a$ equal to about 0.75 of the width of the conduction pathway give a good fit to the data.

cond-mat.mes-hall↗

arXiv2001

Effect of phonon scattering by surface roughness on the universal thermal conductance

The effect of phonon scattering by surface roughness on the thermal conductance in mesoscopic systems at low temperatures is calculated using full elasticity theory. The low frequency behavior of the scattering shows novel power law dependences arising from the unusual properties of the elastic modes. This leads to new predictions for the low temperature depression of the thermal conductance below the ideal universal value. Comparison with the data of Schwab et al. [Nature 404, 974 (2000)] suggests that surface roughness on a scale of the width of the thermal pathway is important in the experiment.

cond-mat.mes-hall↗

arXiv2001

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.

nlin.PS↗

arXiv2001

Nonequilibrium Dynamics in the Complex Ginzburg-Landau Equation

We present results from a comprehensive analytical and numerical study of nonequilibrium dynamics in the 2-dimensional complex Ginzburg-Landau (CGL) equation. In particular, we use spiral defects to characterize the domain growth law and the evolution morphology. An asymptotic analysis of the single-spiral correlation function shows a sequence of singularities -- analogous to those seen for time-dependent Ginzburg-Landau (TDGL) models with O(n) symmetry, where $n$ is even.

cond-mat.stat-mech↗

arXiv2001

Nonequilibrium Dynamics of the Complex Ginzburg-Landau Equation. I. Analytical Results

We present a detailed analytical and numerical study of nonequilibrium dynamics for the complex Ginzburg-Landau (CGL) equation. In particular, we characterize evolution morphologies using spiral defects. This paper (referred to as $\rm I$) is the first in a two-stage exposition. Here, we present analytical results for the correlation function arising from a single-spiral morphology. We also critically examine the utility of the Gaussian auxiliary field (GAF) ansatz in characterizing a multi-spiral morphology. In the next paper of this exposition (referred to as $\rm II$), we will present detailed numerical results.

cond-mat.stat-mech↗

arXiv2000

Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are calculated in a simple scalar model of the elastic waves, and results for long wavelength modes are calculated using the full elasticity theory calculation. We suggest that thin plate elasticty theory provide a useful and tractable approximation to the full three dimensional geometry.

cond-mat.mes-hall↗

arXiv2000

Finite Size Scaling of Domain Chaos

Numerical studies of the domain chaos state in a model of rotating Rayleigh-Benard convection suggest that finite size effects may account for the discrepancy between experimentally measured values of the correlation length and the predicted divergence near onset.

nlin.CD↗

arXiv2000

Simulating Complex Dynamics In Intermediate And Large-Aspect-Ratio Convection Systems

Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of experimental data and the quantitative comparison of theory with experiment, we have developed a three-dimensional finite-difference code that can integrate the three-dimensional Boussinesq equations (which govern the evolution of the temperature, velocity, and pressure fields associated with a convecting flow) efficiently in large box-shaped domains with experimentally appropriate lateral boundary conditions. We discuss some details of this code and present two applications, one to the occurrence of quasiperiodic dynamics with as many as 5 incommensurate frequencies in a moderate-aspect-ratio 10x5 convection cell, and one to the onset of spiral defect chaos in square cells with aspect ratios varying from Gamma=16 to 56.

nlin.PS↗

arXiv1999

Spin Injection in a Ballistic Two-Dimensional Electron Gas

We explore electrically injected, spin polarized transport in a ballistic two-dimensional electron gas. We augment the Buettiker-Landauer picture with a simple, but realistic model for spin-selective contacts to describe multimode reservoir-to-reservoir transport of ballistic spin 1/2 particles. Clear and unambiguous signatures of spin transport are established in this regime, for the simplest measurement configuration that demonstrates them directly. These new effects originate from spin precession of ballistic carriers; they exhibit strong dependence upon device geometry and vanish in the diffusive limit. Our results have important implications for prospective ``spin transistor'' devices.

cond-mat.mes-hall↗

arXiv1998

Turing Instability in a Boundary-fed System

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry-breaking perturbations (Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experiments.

patt-sol↗

arXiv1998

Numerical Bifurcation Diagram for the Two-Dimensional Boundary-fed CDIMA System

We present numerical solution of the chlorine dioxide-iodine-malonic acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from non-symmetry breaking structures along boundary feed gradients to transverse symmetry breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make connection with earlier results and discuss prospects for future work.

patt-sol↗

arXiv1998

Heat Transport in Mesoscopic Systems

Phonon heat transport in mesoscopic systems is investigated using methods analogous to the Landauer description of electrical conductance. A "universal heat conductance" expression that depends on the properties of the conducting pathway only through the mode cutoff frequencies is derived. Corrections due to reflections at the junction between the thermal body and the conducting bridge are found to be small except at very low temperatures where only the lowest few bridge modes are excited. Various non-equilibrium phonon distributions are studied: a narrow band distribution leads to clear steps in the cooling curve, analogous to the quantized resistance values in narrow wires, but a thermal distribution is too broad to show such features.

cond-mat.mes-hall↗

arXiv1997

Controlling Physical Systems with Symmetries

Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are determined by the irreducible representations of the symmetry group of the linearization about the orbit to be controlled. We use the general results to demonstrate the effect of symmetry on the control of two sample physical systems: a coupled map lattice and a particle in a symmetric potential.

chao-dyn↗

arXiv1997

Pinning Control of Spatiotemporal Chaos

Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Qu and Hu. A nonlinear generalization of the method for a 1-d lattice is also presented.

chao-dyn↗

arXiv1997

Dynamics of Coupled Maps with a Conservation Law

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are calculated for a set of independent order parameters. Numerical evidence is produced suggesting that the singularity in the density of Lyapunov exponents at $λ=0$ is a reflection of the singularity in the density of Fourier modes (a ``Van Hove'' singularity) and disappears if the conservation law is broken. Applicability of the Lyapunov dimension to the description of spatiotemporal chaos in a system with a conservation law is discussed.

chao-dyn↗

arXiv1995

Perturbation of Tunneling Processes by Mechanical Degrees of Freedom in Mesoscopic Junctions

We investigate the perturbation in the tunneling current caused by non-adiabatic mechanical motion in a mesoscopic tunnel junction. A theory introduced by Caroli et al. \cite{bi1,bi2,bi3} is used to evaluate second order self-energy corrections for this non-equilibrium situation lacking translational invariance. Inelastic signatures of the mechanical degrees of freedom are found in the current-voltage $I(V)$ characteristics. These give rise to sharp features in the derivative spectrum, $d^2I/dV^2$.

cond-mat↗

arXiv1995

Domain Coarsening in Systems Far from Equilibrium

The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from the inverse width of the Fourier spectrum is studied for both potential and nonpotential models. The morphology of the domains and the defect structures are however quite different in the two cases, and evidence is presented for a second length scale in the nonpotential case.

patt-sol↗