International Journal of Modern Physics B

This foreword is to introduce the reason for this special issue of the journal. Professor Vasudev Mangesh (Nitant) Kenkre has had a distinguished career as a statistical physicist, teacher, educator and a magnet for a great many statistical physicists from around the world across nearly five decades. This volume is to celebrate Nitant’s work. The contributors are mostly his former students, friends and collaborators. This foreword captures a fraction of what Nitant means to us.

Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior.

Hantavirus outbreaks in the American Southwest are hypothesized to be driven by episodic seasonal events of high precipitation, promoting rapid increases in virus-reservoir rodent species that then move across the landscape from high quality montane forested habitats (refugia), eventually over-running human residences and increasing disease risk. In this study, the velocities of rodents and virus diffusion wave propagation and retraction were documented and quantified in the sky-islands of northern New Mexico and related to rodent-virus relationships in refugia versus nonrefugia habitats. Deer mouse (Peromyscus maniculatus) refugia populations exhibited higher Sin Nombre Virus (SNV) infection prevalence than nonrefugia populations. The velocity of propagating diffusion waves of Peromyscus from montane to lower grassland habitats was measured at $24.6\pm 5.6$ m/day (SE), with wave retraction velocities of $28\pm 8.4$ m/day. SNV infection diffusion wave propagation velocity within a deer mouse population averaged $27.5\pm 7.8$ m/day, with a faster retraction wave velocity of $161.5\pm 80.7$ m/day. A spatio-temporal analysis of human Hantavirus Pulmonary Syndrome (HPS) cases during the initial 1993 epidemic revealed a positive linear relationship between the time during the epidemic and the distance of human cases from the nearest deer mouse refugium, with a landscape diffusion wave velocity of $19.6\pm 1.0$ m/day ($r^2=0.96$). These consistent diffusion propagation wave velocity results support the traveling wave component of the HPS outbreak theory and can provide information on space–time constraints for future outbreak forecasts.

The nonlinear dimer obtained through the nonlinear Schrödinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective ${\varphi }^4$ model. In this later context, the self-trapping transition is an initial condition-dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition that has been investigated analytically and mathematically is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of this work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the nondegenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.

The dynamical behavior of a modified Yaldram–Khan model for the catalytic reduction of NO on a surface is studied by Kinetic Monte Carlo simulations. In this modified model, temperature effects are incorporated as desorption rates of the N and CO species. How the presence of contaminants in the gas phase affects the catalytic process is also analyzed by including impurities that can be adsorbed on the lattice and once there remain inert. When N desorption is included, a reactive window appears that is not present in the original YK model on a square lattice. When CO desorption is added large fluctuations appear in the coverages, the system can take a long time to stabilize, during this period, a long lasting reactive state exists that disappears when the stability is reached. When nondesorbing impurities are added, the discontinuous transition to a CO poisoned phase that presents the original YK model disappears, the coverages become continuous, and a nonreactive steady-state is rapidly reached.

In this paper, we discuss coherent atomic oscillations between two weakly coupled Bose–Einstein condensates that are energetically different. The weak link is notionally provided by a laser barrier in a (possibly asymmetric) multi-well trap or by Raman coupling between condensates in different hyperfine levels. The resultant boson Josephson junction dynamics is described by a double-well nonlinear Gross–Pitaevskii equation. On the basis of a new set of Jacobian elliptic function solutions, we describe the period of the oscillations as well as associated quantities and predict novel observable consequences of the interplay of the energy difference and initial phase difference between the two condensate populations.

The microscopic origin of friction is an important topic in science and technology. To date, noteworthy aspects of it remain unsolved. In an effort to shed some light on the possible mechanisms that could give rise to the macroscopic emergence of friction, a very simple 1D system of two particles is considered, one of them is free but moving with an initial velocity, and the other confined by a harmonic potential. The two particles interact via a repulsive Gaussian potential. While it represents in a straightforward manner a tip substrate system in the real world, no analytic solutions can be found for its motion. Because of the interaction, the free particle (tip) may overcome the bound particle (substrate) losing part of its kinetic energy. We solve Newton’s equations of the two particles numerically and calculate the net exchange of energy in the asymptotic state in terms of the relevant parameters of the problem. The effective dissipation that emerges from this simple, classical model with no ad hoc terms shows, surprisingly, a range of rich, nontrivial, behavior. We give theoretical reasoning which provides a satisfactory qualitative description. The essential ingredient of that reasoning is that the transfer of energy from the incoming particle to the confined one can be regarded as the source of the emergent dissipation force the friction experienced by the incoming particle.

Traditional epidemic models consider that individual processes occur at constant rates; an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption indeed fails for almost all infectious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We presented some years ago a general treatment for an SIRS model in which both the infected and the immune phases admit such a description, where the system shows transitions between endemic and oscillating situations. In the present contribution, we consider the effect of seasonality on the transmission rate. Performing numerical simulations of the delayed equations plus seasonality, we have found a rich and complex scenario of oscillations that could be relevant in real epidemics.

In this paper, we analyze a model of an animal feeding on fruits and dispersing their seeds, which are later deposited and capable of germination. The deposition of seeds away from their collection sites produces a delay in the dynamics, whose analytical modeling complicates the description in a way that would delight Nitant. We have found approximate analytical solutions, as well as numerical ones, but here I will emphasize on a typical physicists rule of thumb argument.

In this paper, an exact description of the statistical motion of active particles in three dimensions is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a nonlocal, in time and space, connecting (memory) function. This couples the rate of change of the probability density of finding the particle at position $x$ at time $t$ with the Laplacian of the probability density at all previous times and to all points in space. Starting from the standard Fokker–Planck-like equation for the probability density of finding an active particle at position $x$ swimming along the direction $\widehat{v}$ at time $t$, we derive in this paper in an exact manner the connecting function that allows a description of active motion in terms of this diffusion equation.

A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective phenomena where discrete scale invariance plays an important role. Here we investigate two distinct approaches towards the general problem of how to detect log-periodic oscillations in arbitrary time series without prior knowledge of the location of the moveable singularity. We first show that the problem has a definite solution in Fourier space; however, the technique involved requires an unrealistically large signal-to-noise ratio. Then we show that the quadrature signal obtained via analytic continuation onto the imaginary axis, using the Hilbert transform, necessarily retains the log-periodicities found in the original signal. This finding allows the development of a new method of detecting log-periodic oscillations that relies on calculation of the instantaneous phase of the analytic signal. We then illustrate the method by applying it to the stock market crash of 1987 and explore the important role played by positive feedback mechanisms in relation to economic bubble formation, financial crashes, log-periodic dynamics and analytic behavior. Finally, we discuss the relevance of these findings for parametric rather than nonparametric estimation of critical times.

A particle roaming in a potential in the presence of spatial heterogeneities such as traps or physical barriers is a mathematical representation of a vast number of processes across multiple disciplines, ranging from the dynamics of chemical reactions and the movement of foraging animals to the performance of a financial asset. Among the approaches to tackle such problems, a powerful one is the so-called defect technique. Within a continuous space–time formulation, the technique has been successfully used to analyze diffusion problems with partially absorbing boundaries, but has not been employed to study other types of boundaries. Here we exploit the continuity equation to extend the defect technique to when partially reflecting barriers are present. For each boundary type, we apply the defect formalism to the Ornstein–Uhlenbeck process, recovering known analytical results and presenting new ones.

It is a great pleasure to be part of the celebration of Nitant Kenkre’s scientific career. In this paper, we review mathematical models for studying evolutionary branching and diversification in biology. We highlight insights provided by Nitant Kenkre’s work in the early 2000s as part of the Consortium of the Americas for Interdisciplinary Science. We focus on the use of these models for understanding the conditions that promote phenotypic diversification and innovation in biological systems, understood as the branching of stationary solutions, and some of the ideas that emerged as part of the research Consortium. We highlight recent developments and applications of stochastic, nonlocal partial derivative formalisms.

An established formal way to solve the Liouville equation for dynamical systems with hermitian Hamiltonians is to frame the problem via parametrization in a canonical ensemble. The goal is to solve for the dynamics in the canonical ensemble. This approach allows one to examine temperature-dependent relaxation functions as a part of the construction of the full solution to the Liouville equation. Of course, a full solution to the Liouville equation may not always be necessary as it is the relaxation function which often tends to be of interest. The formalism involves evaluation of infinite continued fractions and this can at times be an especially challenging problem. Here we explore the relaxation function in near-equilibrium systems in the presence of strong nonlinearity. Due to computational challenges, we consider small systems. However, even our small system considerations may be adequate to infer about the relaxation in large systems. We show that the nonlinear systems tend to lead to nonconvergent infinite continued fractions. These continued fractions cannot be approximated perturbatively. We close by presenting a new strategy to evaluate them, thereby demonstrating a successful way to examine relaxation processes in strongly nonlinear systems.

A distinctive fishtail feature in multifractal spectra derived from heart rate variability (HRV) data closely resembles similar features in plots of the Gibbs free energy versus reduced pressure for a van der Waals fluid below the critical temperature, and, in analogy to the nonideal fluid, signals a phase transition from one multifractal state to another. This fishtail feature, often overlooked or dismissed in previous studies, is observed most prevalently in unhealthy patients and suggests a realignment between multifractal variables and their thermodynamic analogs. The van der Waals analogy and subsequent alternate interpretation of multifractal variables and functions lead one to construct a three-dimensional heart health phase diagram reminiscent of a $P-V-T$ diagram for the van der Waals fluid. The diagram which makes use of the Maxwell width as a measure of heart health produces an orderly progression from healthy to unhealthy.

In this paper, we investigate signatures of variation in the behavior of correlated time series by analyzing changes in the topological properties of the corresponding visibility graph. Variations in six different network measures: assortativity, average path length, clustering, transitivity, density, and the average of the mean link length, are explored. We construct visibility graphs from the original and the magnitude and sign of its increment series. Both the horizontal and the natural visibility graphs are studied. Through extensive numerical studies on the time series of fractional Brownian motion (fBm), we first identify network measures that can reflect the changes in correlations in the time series. The efficacy of these markers is examined to identify the transitions in two systems, a two-dimensional (2D) Ising spin system and EEG data with seizures. While all the identified network measures capture the change in the thermal equilibrium correlations for the Ising spin system, they have limited success in the case of the time-dependent fluctuations in the EEG data. We identify some markers relevant to detecting seizures in the EEG data set.