arXiv subjects

K. Lindenberg

Publications and source records attributed to K. Lindenberg.

At least 19 recordsLinked to original sources

arXiv2015

Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.

cond-mat.stat-mech↗

arXiv2014

A reaction-subdiffusion model of fluorescence recovery after photobleaching (FRAP)

Anomalous diffusion, in particular subdiffusion, is frequently invoked as a mechanism of motion in dense biological media, and may have a significant impact on the kinetics of binding/unbinding events at the cellular level. In this work we incorporate anomalous diffusion in a previously developed model for FRAP experiments. Our particular implementation of subdiffusive transport is based on a continuous time random walk (CTRW) description of the motion of fluorescent particles, as CTRWs lend themselves particularly well to the inclusion of binding/unbinding events. In order to model switching between bound and unbound states of fluorescent subdiffusive particles, we derive a fractional reaction-subdiffusion equation of rather general applicability. Using suitable initial and boundary conditions, this equation is then incorporated in the model describing two-dimensional kinetics of FRAP experiments. We find that this model can be used to obtain excellent fits to experimental data. Moreover, recovery curves corresponding to different radii of the circular bleach spot can be fitted by a single set of parameters. While not enough evidence has been collected to claim with certainty that CTRW is the underlying transport mechanism in FRAP experiments, the compatibility of our results with experimental data fuels the discussion as to whether normal diffusion or anomalous diffusion is the appropriate model, and as to whether anomalous diffusion effects are important to fully understand the outcomes of FRAP experiments. On a more technical side, we derive explicit analytic solutions of our model in certain limits.

cond-mat.stat-mech↗

arXiv2013

Measurement of the 92,93,94,100Mo(g,n) reactions by Coulomb Dissociation

The Coulomb Dissociation (CD) cross sections of the stable isotopes 92,94,100Mo and of the unstable isotope 93Mo were measured at the LAND/R3B setup at GSI Helmholtzzentrum f\"ur Schwerionenforschung in Darmstadt, Germany. Experimental data on these isotopes may help to explain the problem of the underproduction of 92,94Mo and 96,98Ru in the models of p-process nucleosynthesis. The CD cross sections obtained for the stable Mo isotopes are in good agreement with experiments performed with real photons, thus validating the method of Coulomb Dissociation. The result for the reaction 93Mo(g,n) is especially important since the corresponding cross section has not been measured before. A preliminary integral Coulomb Dissociation cross section of the 94Mo(g,n) reaction is presented. Further analysis will complete the experimental database for the (g,n) production chain of the p-isotopes of molybdenum.

astro-ph.IM↗

arXiv2013

On the non-equivalence of two standard random walks

We focus on two models of nearest-neighbour random walks on d-dimensional regular hyper-cubic lattices that are usually assumed to be identical - the discrete-time Polya walk, in which the walker steps at each integer moment of time, and the Montroll-Weiss continuous-time random walk in which the time intervals between successive steps are independent, exponentially and identically distributed random variables with mean 1. We show that while for symmetric random walks both models indeed lead to identical behaviour in the long time limit, when there is an external bias they lead to markedly different behaviour.

cond-mat.stat-mech↗

arXiv2012

Speeding chemical reactions by focusing

We present numerical results for a chemical reaction of colloidal particles which are transported by a laminar fluid and are focused by periodic obstacles in such a way that the two components are well mixed and consequently the chemical reaction is speeded up. The roles of the various system parameters (diffusion coefficients, reaction rate, obstacles sizes) are studied. We show that focusing speeds up the reaction from the diffusion limited rate (t to the power -1/2) to very close to the perfect mixing rate, (t to the power -1).

physics.chem-ph↗

arXiv2011

Asymptotic solutions of decoupled continuous-time random walks with superheavy-tailed waiting time and heavy-tailed jump length distributions

We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a non-degenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$-function and find its behavior for small and large distances.

cond-mat.stat-mech↗

arXiv2010

Application of Fractional Calculus to Reaction-Subdiffusion Processes and Morphogen Gradient Formation

It is a well known fact that subdiffusion equations in terms of fractional derivatives can be obtained from Continuous Time Random Walk (CTRW) models with long-tailed waiting time distributions. Over the last years various authors have shown that extensions of such CTRW models incorporating reactive processes to the mesoscopic transport equations may lead to non-intuitive reaction-subdiffusion equations. In particular, one such equation has been recently derived for a subdiffusive random walker subject to a linear (first-order) death process. We take this equation as a starting point to study the developmental biology key problem of morphogen gradient formation, both for the uniform case where the morphogen degradation rate coefficient (reactivity) is constant and for the non-uniform case (position-dependent reactivity). In the uniform case we obtain exponentially decreasing stationary concentration profiles and we study their robustness with respect to perturbations in the incoming morphogen flux. In the non-uniform case we find a rich phenomenology at the level of the stationary profiles. We conclude that the analytic form of the long-time morphogen concentration profiles is very sensitive to the spatial dependence of the reactivity and the specific value of the anomalous diffusion coefficient.

physics.bio-ph↗

arXiv2008

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $ρ$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^γ$ with $0\leq γ\leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $γ\leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $γ> 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $γ$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous.

cond-mat.stat-mech↗

arXiv2008

Noise-induced phase transitions in field-dependent relaxational dynamics: The Gaussian ansatz

We present an analytic mean field theory for relaxational dynamics in spatially extended systems that undergo purely noise-induced phase transitions to ordered states. The theory augments the usual mean field approach with a Gaussian ansatz that yields quantitatively accurate results for strong coupling. We obtain analytic results not only for steady state mean fields and distribution widths, but also for the dynamical approach to a steady state or to collective oscillatory behaviors in multi-field systems. Because the theory yields dynamical information, it can also predict the initial-condition-dependent final state (disordered state, steady or oscillatory ordered state) in multistable arrays.

cond-mat.stat-mech↗

arXiv2006

Intermittent random walks for an optimal search strategy: One-dimensional case

We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is the maximal time the search process is allowed to run. With probability αthe searchers step on a nearest-neighbour, and with probability (1-α) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P_N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P_N is a non-monotonic function of α, and show that there is an optimal choice α_{opt}(N) of αwell within the intermittent regime, 0 < α_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to the "pure" random walk cases α=0 and α= 1.

cond-mat.stat-mech↗

arXiv2006

Variational band theory of vibronic polarons in crystals. II. Extending Merrifield's Ansatz

Merrifield's Variational Ansatz is extended so as to cover the case of two electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of the local and kinetic (hopping) energies in the absence of vibrations, the vibrational energy, and a mixing band-off-diagonal part linear in the electron-phonon coupling, all expressed in second quantization terms. The variational eigenstate is a linear combination of Merrifield states for either electronic band. We derive equations for the phonon Fourier amplitudes and for the fractional contribution of either electronic band.

cond-mat.supr-con↗

arXiv2005

Itinerant vibronic polarons: A Merrifield approach I. Low energy range calculations

We extend Merrifield's Variational Ansatz in the variational band theory of polarons to cover a frame of two electronic bands mixed by an Einstein phonon. The Hamiltonian is composed of the local and hopping energy terms, the vibrational energy, and a band-mixing term linear in the electron-phonon coupling. The eigenstate is a linear combination of Merrifield states in either electron band. The variational equations are solved numerically, so as to obtain the energy vs. momentum relation in ground state. Our variational method generates either Jahn-Teller polarons if the electronic bands degenerate or Pseudo-Jahn-Teller polarons if they nearly degenerate, both entities regarded as likely carriers in metal-oxide manifolds of high-Tc superconducting cuprates and colossal magnetoresistance exhibiting manganates.

cond-mat.supr-con↗

arXiv2004

From subdiffusion to superdiffusion of particles on solid surfaces

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending on the potential and the damping, we observe superdiffusion, large-step diffusion, diffusion, and subdiffusion. Superdiffusive behavior is associated with low damping and is in most cases transient, albeit often long. Subdiffusive behavior is associated with highly damped particles in random potentials. In some cases subdiffusive behavior persists over our entire simulation and may be characterized as metastable. In any case, we stress that this rich variety of behaviors emerges naturally from an ordinary Langevin equation for a system described by ordinary canonical Maxwell-Boltzmann statistics.

cond-mat.stat-mech↗

arXiv2003

Diffusion on a solid surface: Anomalous is normal

We present a numerical study of classical particles diffusing on a solid surface. The particles' motion is modeled by an underdamped Langevin equation with ordinary thermal noise. The particle-surface interaction is described by a periodic or a random two dimensional potential. The model leads to a rich variety of different transport regimes, some of which correspond to anomalous diffusion such as has recently been observed in experiments and Monte Carlo simulations. We show that this anomalous behavior is controlled by the friction coefficient, and stress that it emerges naturally in a system described by ordinary canonical Maxwell-Boltzmann statistics.

cond-mat.stat-mech↗

arXiv2001

Diffusion-Limited Reaction in One Dimension: Paired and Unpaired Nucleation

We consider the dynamics of diffusing particles in one space dimension with annihilation on collision and nucleation (creation of particles) with constant probability per unit time and length. The cases of nucleation of single particles and nucleation in pairs are considered. A new method of analysis permits exact calculation of the steady state density and its time evolution in terms of the three parameters describing the microscopic dynamics: the nucleation rate, the initial separation of nucleated pairs and the diffusivity of a particle. For paired nucleation at sufficiently small initial separation the nucleation rate is proportional to the square of the steady state density. For unpaired nucleation, and for paired nucleation at sufficiently large initial separation, the nucleation rate is proportional to the cube of the steady state density.

cond-mat.stat-mech↗

arXiv2001

Thermal Resonance in Signal Transmission

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.

cond-mat.stat-mech↗

arXiv2001

On the Collective Behavior of Parametric Oscillators

We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is a detailed characterization of the motions underlying these instabilities. This presentation includes regimes not identified in earlier work [I. Bena and C. Van den Broeck, Europhys. Lett. {\bf 48}, 498 (1999)]. In addition to the familiar parametric instability of individual oscillators, two kinds of collective instabilities are identified. In one the mean amplitude diverges monotonically while in the other the divergence is oscillatory. The frequencies of collective oscillatory instabilities in general bear no simple relation to the eigenfrequencies of the individual oscillators nor to the frequency of the external modulation. Numerical simulations show that systems with only nearest neighbor coupling have collective instabilities similar to those of the mean field model. Many of the mean field results are already apparent in a simple dimer [M. Copelli and K. Lindenberg, to appear in Phys. Rev. E].

cond-mat.stat-mech↗

arXiv2000

Harvesting Thermal Fluctuations: Activation Process Induced by a Nonlinear Chain in Thermal Equilibrium

We present a model in which the immediate environment of a bistable system is a molecular chain which in turn is connected to a thermal environment of the Langevin form. The molecular chain consists of masses connected by harmonic or by anharmonic springs. The distribution, intensity, and mobility of thermal fluctuations in these chains is strongly dependent on the nature of the springs and leads to different transition dynamics for the activated process. Thus, all else (temperature, damping, coupling parameters between the chain and the bistable system) being the same, the hard chain may provide an environment described as diffusion-limited and more effective in the activation process, while the soft chain may provide an environment described as energy-limited and less effective. The importance of a detailed understanding of the thermal environment toward the understanding of the activation process itself is thus highlighted.

cond-mat.stat-mech↗