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We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…
For $\lambda>0$, we define a $\lambda$-damped random walk to be a random walk that is started from a random vertex of a graph and stopped at each step with probability $\frac{\lambda}{1+\lambda}$, otherwise continued with probability…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
We develop a general geometric method to establish the existence of positive Lyapunov exponents for a class of skew products. The technique is applied to show non-uniform hyperbolicity of some conservative partially hyperbolic…
We design the controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a…
In this paper, we derive new passive maps akin to incremental passive maps, for a class of nonlinear systems using dynamic feedback and Krasovskii's method. Further using the passive maps we present a control methodology for stabilization…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
Within the quantum field-theoretical approach describing the evolution of a quadratic Liouvillian in the basis of Keldysh contour coherent states, we investigate the spectral and transport properties of a dissipative superconducting system…
Although the electrical transport properties of mesoscopic metallic samples have been investigated extensively over the past two decades, the thermal properties have received far less attention. This may be due in part to the difficulty of…
Route-level travel time reliability requires characterizing the distribution of total travel time across correlated segments -- a problem where existing methods either assume independence (fast but miscalibrated) or model dependence via…
In contrast to equilibrium systems, non-equilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber and heat bath rates, we illustrate this expectation for an Ising lattice…
The majority vote model is one of the simplest opinion systems yielding distinct phase transitions and has garnered significant interest in recent years. However, its original formulation is not, in general, thermodynamically consistent,…
In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear…
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property…
Electronic transport through a two-level system driven by external electric field and coupled to (magnetic or non-magnetic) electron reservoirs is considered theoretically. The basic transport characteristics such as current and tunnel…
In this paper, we study the differentiability of SRB measures for partially hyperbolic systems. We show that for any $s \geq 1$, for any integer $\ell \geq 2$, any sufficiently large $r$, any $\varphi \in C^{r}(\T, \R)$ such that the map $f…
Quenched disorders can strongly influence the physical properties of quantum many-body systems. The real-space strong-disorder renormalization group (SDRG) analysis has shown that the spin-1/2 random Heisenberg chain is controlled by the…
For students familiar with equilibrium statistical mechanics, the notion of a positive specific heat, being intimately related to the idea of stability, is both intuitively reasonable and mathematically provable. However, for system in…
This work presents a computationally lightweight motion planner for over-actuated platforms. For this purpose, a general state-space model for mobile platforms with several kinematic chains is defined, which considers non-linearities and…
In this paper, several advanced data-driven nonlinear identification techniques are compared on a specific problem: a simplified glucoregulatory system modeling example. This problem represents a challenge in the development of an…