arXiv subjects

Katja Lindenberg

Publications and source records attributed to Katja Lindenberg.

At least 55 records · Page 3Linked to original sources

arXiv2009

Energy Transport in a One-Dimensional Granular Gas

We study heat conduction in one-dimensional granular gases. In particular, we consider two mechanisms of viscous dissipation during inter-grain collisions. In one, the dissipative force is proportional to the grain's velocity and dissipates not only energy but also momentum. In the other, the dissipative force is proportional to the relative velocity of the grains and therefore conserves momentum even while dissipating energy. This allows us to explore the role of momentum conservation in the heat conduction properties of this one-dimensional nonlinear system. We find normal thermal conduction whether or not momentum is conserved.

cond-mat.stat-mech↗

arXiv2009

Universality of efficiency at maximum power

We investigate the efficiency of power generation by thermo-chemical engines. For strong coupling between the particle and heat flows and in the presence of a left-right symmetry in the system, we demonstrate that the efficiency at maximum power displays universality up to quadratic order in the deviation from equilibrium. A maser model is presented to illustrate our argument.

cond-mat.stat-mech↗

arXiv2008

Short Pulse Dynamics in Strongly Nonlinear Dissipative Granular Chains

We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, is dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.

cond-mat.soft↗

arXiv2008

Thermoelectric efficiency at maximum power in a quantum dot

We identify the operational conditions for maximum power of a nanothermoelectric engine consisting of a single quantum level embedded between two leads at different temperatures and chemical potentials. The corresponding thermodynamic efficiency agrees with the Curzon-Ahlborn expression up to quadratic terms in the gradients, supporting the thesis of universality beyond linear response.

cond-mat.stat-mech↗

arXiv2008

Continuous time random walk for open systems: Fluctuation theorems and counting statistics

We consider continuous time random walks (CTRW) for open systems that exchange energy and matter with multiple reservoirs. Each waiting time distribution (WTD) for times between steps is characterized by a positive parameter a, which is set to a=1 if it decays at least as fast as t^{-2} at long times and therefore has a finite first moment. A WTD with a<1 decays as t^{-a-1}. A fluctuation theorem for the trajectory quantity R, defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory, holds for any CTRW. However, R can be identified as a trajectory entropy change only if the WTDs have a=1 and satisfy separability (also called "direction time independence"). For nonseparable WTDs with a=1, R can only be identified as a trajectory entropy change at long times, and a fluctuation theorem for the entropy change then only holds at long times. For WTDs with 0<a<1 no meaningful fluctuation theorem can be derived. We also show that the (experimentally accessible) n'th moments of the energy and matter transfers between the system and a given reservoir grow as t^{n a} at long times.

cond-mat.stat-mech↗

arXiv2008

Number of distinct sites visited by a subdiffusive random walker

The asymptotic mean number of distinct sites visited by a subdiffusive continuous time random walker in two dimensions seems not to have been explicitly calculated anywhere in the literature. This number has been calculated for other dimensions for only one specific asymptotic behavior of the waiting time distribution between steps. We present an explicit derivation for two cases in all integer dimensions so as to formally complete a tableaux of results. In this tableaux we include the dominant as well as subdominant contributions in all integer dimensions. Other quantities that can be calculated from the mean number of distinct sites visited are also discussed.

cond-mat.stat-mech↗

arXiv2007

The subdiffusive target problem: Survival probability

The asymptotic survival probability of a spherical target in the presence of a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a continuous Euclidean medium is calculated. In one and two dimensions the survival probability of the target in the presence of a single trap decays to zero as a power law and as a power law with logarithmic correction, respectively. The target is thus reached with certainty, but it takes the trap an infinite time on average to do so. In three dimensions a single trap may never reach the target and so the survival probability is finite and, in fact, does not depend on whether the traps move diffusively or subdiffusively. When the target is surrounded by a sea of traps, on the other hand, its survival probability decays as a stretched exponential in all dimensions (with a logarithmic correction in the exponent for $d=2$). A trap will therefore reach the target with certainty, and will do so in a finite time. These results may be directly related to enzyme binding kinetics on DNA in the crowded cellular environment.

cond-mat.stat-mech↗

arXiv2007

Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators

We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time averaged frequencies and mean field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population.

cond-mat.stat-mech↗

arXiv2006

Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Phys. Rev. E Vol. 74, 021117 (2006), we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

physics.class-ph↗

arXiv2006

Dispersionless transport in a washboard potential

We study and characterize a new dynamical regime of underdamped particles in a tilted washboard potential. We find that for small friction in a finite range of forces the particles move essentially nondispersively, that is, coherently, over long intervals of time. The associated distribution of the particle positions moves at an essentially constant velocity and is far from Gaussian-like. This new regime is complementary to, and entirely different from, well-known nonlinear response and large dispersion regimes observed for other values of the external force.

cond-mat.stat-mech↗

arXiv2006

Effects of Disorder on Synchronization of Discrete Phase-Coupled Oscillators

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2, 3, 4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width. Even in the presence of transition rate disorder, numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength. Numerical simulations make possible the further characterization of the synchronized arrays.

cond-mat.stat-mech↗

arXiv2006

Simulations for trapping reactions with subdiffusive traps and subdiffusive particles

While there are many well-known and extensively tested results involving diffusion-limited binary reactions, reactions involving subdiffusive reactant species are far less understood. Subdiffusive motion is characterized by a mean square displacement $ \sim t^γ$ with $0<γ<1$. Recently we calculated the asymptotic survival probability $P(t)$ of a (sub)diffusive particle ($γ^\prime$) surrounded by (sub)diffusive traps ($γ$) in one dimension. These are among the few known results for reactions involving species characterized by different anomalous exponents. Our results were obtained by bounding, above and below, the exact survival probability by two other probabilities that are asymptotically identical (except when $γ^\prime=1$ and $0<γ<2/3$). Using this approach, we were not able to estimate the time of validity of the asymptotic result, nor the way in which the survival probability approaches this regime. Toward this goal, here we present a detailed comparison of the asymptotic results with numerical simulations. In some parameter ranges the asymptotic theory describes the simulation results very well even for relatively short times. However, in other regimes more time is required for the simulation results to approach asymptotic behavior, and we arrive at situations where we are not able to reach asymptotia within our computational means. This is regrettably the case for $γ^\prime=1$ and $0<γ<2/3$, where we are therefore not able to prove or disprove even conjectures about the asymptotic survival probability of the particle.

cond-mat.stat-mech↗

arXiv2006

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front.

cond-mat.soft↗

arXiv2006

The target problem with evanescent subdiffusive traps

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time.

cond-mat.soft↗

arXiv2006

Critical behavior and synchronization of discrete stochastic phase coupled oscillators

Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, we explicitly rule out multistability and show that that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents βand ν, a lower critical dimension d_{lc} = 2, and an upper critical dimension d_{uc}=4.

cond-mat.stat-mech↗

arXiv2006

Properties of the reaction front in a reaction-subdiffusion process

We study the reaction front for the process $A+B\to C$ in which the reagents move subdiffusively. We propose a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. Scaling solutions to these equations are presented and compared with those of a direct numerical integration of the equations. We find that for reactants whose mean square displacement varies sublinearly with time as $ \sim t^γ$, the scaling behaviors of the reaction front can be recovered from those of the corresponding diffusive problem with the substitution $t\to t^γ$

cond-mat.stat-mech↗

arXiv2006

Trapping reactions with subdiffusive traps and particles

Reaction dynamics involving subdiffusive species is an interesting topic with only few known results, especially when the motion of different species is characterized by different anomalous diffusion exponents. Here we study the reaction dynamics of a (sub)diffusive particle surrounded by a sea of (sub)diffusive traps in one dimension. Under some reasonable assumptions we find rigorous results for the asymptotic survival probability of the particle in most cases, but have not succeeded in doing so for a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.

cond-mat.soft↗

arXiv2005

An analytical approach to sorting in periodic potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

cond-mat.soft↗