Weak disorder: anomalous transport and diffusion are normal yet again

Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around a critical force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here we show that beyond a simple enhancement lies a much more interesting phenomenology. For some parameter regimes the system exhibits a rich variety of behaviors from normal diffusion to superdiffusion, subdiffusion and even subtransport.Comment: Substantial improvements in presentatio

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.Comment: 6 pages. References added, improved account of previous results and typos correcte

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

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

Trapping reactions with subdiffusive traps and particles characterized by different anomalous diffusion exponents

A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in ordinary diffusion is replaced by t^gamma. However, very few results are known for reactions involving different species 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. We find rigorous results for the asymptotic survival probability of the particle in most cases, with the exception of the case of a particle that diffuses normally while the anomalous diffusion exponent of the traps is smaller than 2/3.Comment: To appear in Phys. Rev.

On the occurrence of oscillatory modulations in the power-law behavior of dynamic and kinetic processes in fractals

The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical processes, which as a consequence of the time evolution develop a characteristic length of the form $\xi \propto t^{1/z}$, where z is the dynamic exponent. So, we conjecture that the interplay between the physical process and the symmetry properties of the fractal leads to the occurrence of time DSI evidenced by soft log-periodic modulations of physical observables, with a fundamental time scaling ratio given by $\tau = b_1 ^z$. The conjecture is tested numerically for random walks, and representative systems of broad universality classes in the fields of irreversible and equilibrium critical phenomena.Comment: 6 pages, 3 figures. Submitted to EP

The Relationship between Brachycephalic Head Features in Modern Persian Cats and Dysmorphologies of the Skull and Internal Hydrocephalus

Background: Cat breeders observed a frequent occurrence of internal hydrocephalus in Persian cats with extreme brachycephalic head morphology. Objective: To investigate a possible relationship among the grade of brachycephaly, ventricular dilatation, and skull dysmorphologies in Persian cats. Animals: 92 Persian-, 10 Domestic shorthair cats. Methods: The grade of brachycephaly was determined on skull models based on CT datasets. Cranial measurements were examined with regard to a possible correlation with relative ventricular volume, and cranial capacity. Persians with high (peke-face Persians) and lower grades of brachycephaly (doll-face Persians) were investigated for the presence of skull dysmorphologies. Results: The mean cranial index of the peke-face Persians (0.97 ± 0.14) was significantly higher than the mean cranial index of doll-face Persians (0.66 ± 0.04; P < 0.001). Peke-face Persians had a lower relative nasal bone length (0.15 ± 0.04) compared to doll-face (0.29 ± 0.08; P < 0.001). The endocranial volume was significantly lower in doll-face than peke-face Persians (89.6 ± 1.27% versus 91.76 ± 2.07%; P < 0.001). The cranial index was significantly correlated with this variable (Spearman´s r: 0.7; P < 0.0001). Mean ventricle: Brain ratio of the peke-face group (0.159 ± 0.14) was significantly higher compared to doll-face Persians (0.015 ± 0.01; P < 0.001). Conclusion and Clinical Relevance: High grades of brachycephaly are also associated with malformations of the calvarial and facial bones as well as dental malformations. As these dysmorphologies can affect animal welfare, the selection for extreme forms of brachycephaly in Persian cats should be reconsidered

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