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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. [ABSTRACT FROM AUTHOR]

Here, the dynamics of inverse tapered granular chains, which are alignments of beads with progressively increasing radii, are investigated. These chains are subjected to harmonic excitation by a moving wall and probed at the tapered end. Intermediate taperings using Ni-Ti (metal) and Teflon (plastic) granules are considered. The proposed chain is based on the frequency responses. The incident signal is set between 1 Hz and 3 kHz. The system transmits or filters incident signals at low or high driving frequencies, respectively. For intermediate frequencies, similar to the human voice and most musical instruments, the driving frequency is amplified, presenting a median gain of 24 dB (an increase in energy by a factor of 250) over long durations. A transition map, showing regions of transmission, amplification, and filtration as a function of driving amplitude and frequency, is provided. This system could serve as a starting point for studies on natural voice amplifiers, which are important for addressing hearing loss and vocal disorders, as well as other applications requiring mechanical signal amplification. The findings suggest that a proper granular arrangement could enable the amplification of low or extremely low driving frequencies. [ABSTRACT FROM AUTHOR]

The present study describes a way to control the dispersion of an impulse in a two-dimensional square granular crystal with tapered beads. The control is through the redirection of the characteristic load transfer path by controlling the shape of the scattering of wavefront. The main goal is to contribute to the development of appropriately designed granular media to mitigate impacts. The crystal is constituted of spherical granules with a wide range of radii. Interstitial particles are strategically positioned to allow a large number of collisions per unit area. The waves are produced by a striker that collides against the crystal. We analyze how material combinations, number of layers, tapering parameter, and disorder affect the decay of the wave amplitude. Our studies suggest that ∼90% impulse attenuation can be accomplished using a system thickness of 5 grains. [ABSTRACT FROM AUTHOR]

We study how the dynamics of solitary wave (SW) interactions in integrable systems is different from that in nonintegrable systems in the context of crossing of two identical SWs in the (integrable) Toda and the (non-integrable) Hertz systems. We show that the collision process in the Toda system is perfectly symmetric about the collision point, whereas in the Hertz system, the collision process involves more complex dynamics. The symmetry in the Toda system forbids the formation of secondary SWs (SSWs), while the absence of symmetry in the Hertz system allows the generation of SSWs. We next show why the experimentally observed by-products of SW–SW interactions, the SSWs, must form in the Hertz system. We present quantitative estimations of the amount of energy that transfers from the SW after collision to the SSWs using (i) dynamical simulations, (ii) a phenomenological approach using energy and momentum conservation, and (iii) using an analytical solution introduced earlier to describe the SW in the Hertz system. We show that all three approaches lead to reliable estimations of the energy in the SSWs. [ABSTRACT FROM AUTHOR]

Rapid absorption of impulses using light-weight, small, reusable systems is a challenging problem. An axially aligned set of progressively shrinking elastic spheres, a “tapered chain,” has been shown to be a versatile and scalable shock absorber in earlier simulational, theoretical, and experimental works by several authors. We have recently shown (see R. L. Doney and S. Sen, Phys. Rev. Lett. 97, 155502 (2006)) that the shock absorption ability of a tapered chain can be dramatically enhanced by placing small interstitial grains between the regular grains in the tapered chain systems. Here we focus on a detailed study of the problem introduced in the above mentioned letter, present extensive dynamical simulations using parameters for a titanium-aluminum-vanadium alloy Ti6Al4V, derive attendant hard-sphere analyses based formulae to describe energy dispersion, and finally discuss some preliminary experimental results using systems with chrome spheres and small Nitinol interstitial grains to present the underlying nonlinear dynamics of this so-called decorated tapered granular alignment. We are specifically interested in small systems, comprised of several grains. This is because in real applications, mass and volume occupied must inevitably be minimized. Our conclusion is that the decorated tapered chain offers enhanced energy dispersion by locking in much of the input energy in the grains of the tapered chain rather than in the small interstitial grains. Thus, the present study offers insights into how the shock absorption capabilities of these systems can be pushed even further by improving energy absorption capabilities of the larger grains in the tapered chains. We envision that these scalable, decorated tapered chains may be used as shock absorbing components in body armor, armored vehicles, building applications and in perhaps even in applications in rehabilitation science. [ABSTRACT FROM AUTHOR]

We examine the long-term behavior of nonintegrable, energy-conserved, one-dimensional systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Such systems can be set up to have no phononic background excitation and represent examples of a sonic vacuum. Existing dynamical studies showed the absence of energy equipartitioning in such systems, hence their long-term dynamics was described as quasiequilibrium. Here we show that these systems do in fact reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. As a by-product, we show how fluctuations of system quantities, and thus the distribution functions, are influenced by the Hertz potential. In particular, the variance of the system's kinetic energy probability density function is reduced by a factor related to the contact potential. [ABSTRACT FROM AUTHOR]

Recent particulate flow research using a discrete element simulation-dynamical systems approach is described. The simulation code used is very efficient and the mathematical model is an integro-partial differential equation. Examples are presented to show the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

Solitary waves in alignment of elastic beads have been an important area of study. An important and rich area has been the behavior of solitary waves at a boundary, where features such as localization, anomalous behavior in scattering and transmission, quasiequilibrium phase, etc. are being studied. An application area of significance is the design of artificial granular alignments for shock decimation and dispersion. In this review article, we first present a summary and background of these unique features, and some designs in 1D which exploit these features. We further discuss some extensions to higher dimensional systems and their impact decimation ability. [ABSTRACT FROM AUTHOR]

The response of a granular alignment held between fixed end walls to an impulse was introduced in the works of Nesterenko between 1983 and the years that followed. He showed analytically and experimentally that a granular chain admits a propagating solitary wave. In his analytic work, under small precompression compared to the local strain, he showed that one finds a propagating solitary wave. The solitary wave was also seen experimentally but at zero and vanishingly small precompressions. Under stronger precompression a possible Korteweg–de Vries (KdV) solitary wave was suggested though never observed. Later, others confirmed the solitary wave result at zero loading. Sen and Manciu reported seeing the solitary wave behavior in numerical simulations and in 2001 proposed an accurate solution which obtained the solitary wave at zero precompression as seen in some experiments and in numerics. Simulations showed an oscillatory tail following the solitary wave at small precompressions. In an experimental study in 1997, Costé, Falcon and Fauve and later Nesterenko et al. reported seeing propagation of a wave with an oscillatory tail. The oscillatory tail eventually consumed the solitary wave with increasing precompression. How can one reconcile Nesterenko's solitary wave for the weakly precompressed system with Sen and Manciu's solitary wave solution for zero precompression? Here we show that there is a separate solitary wave phase at a certain weak but finite loading regime which is distinct from Sen and Manciu's work and this may be the reason why Nesterenko's analytic theory seems to admit a solitary wave at finite loadings. We also offer insights into why the KdV solution is not seen. [ABSTRACT FROM AUTHOR]

Background: Several highly pathogenic avian influenza (AI) outbreaks have been reported over the past decade. South Korea recently faced AI outbreaks whose economic impact was estimated to be 6.3 billion dollars, equivalent to nearly 50% of the profit generated by the poultry-related industries in 2008. In addition, AI is threatening to cause a human pandemic of potentially devastating proportions. Several studies show that a stochastic simulation model can be used to plan an efficient containment strategy on an emerging influenza. Efficient control of AI outbreaks based on such simulation studies could be an important strategy in minimizing its adverse economic and public health impacts.Methods: We constructed a spatio-temporal multi-agent model of chickens and ducks in poultry farms in South Korea. The spatial domain, comprised of 76 (37.5 km x 37.5 km) unit squares, approximated the size and scale of South Korea. In this spatial domain, we introduced 3,039 poultry flocks (corresponding to 2,231 flocks of chickens and 808 flocks of ducks) whose spatial distribution was proportional to the number of birds in each province. The model parameterizes the properties and dynamic behaviors of birds in poultry farms and quarantine plans and included infection probability, incubation period, interactions among birds, and quarantine region.Results: We conducted sensitivity analysis for the different parameters in the model. Our study shows that the quarantine plan with well-chosen values of parameters is critical for minimize loss of poultry flocks in an AI outbreak. Specifically, the aggressive culling plan of infected poultry farms over 18.75 km radius range is unlikely to be effective, resulting in higher fractions of unnecessarily culled poultry flocks and the weak culling plan is also unlikely to be effective, resulting in higher fractions of infected poultry flocks.Conclusions: Our results show that a prepared response with targeted quarantine protocols would have a high probability of containing the disease. The containment plan with an aggressive culling plan is not necessarily efficient, causing a higher fraction of unnecessarily culled poultry farms. Instead, it is necessary to balance culling with other important factors involved in AI spreading. Better estimations for the containment of AI spreading with this model offer the potential to reduce the loss of poultry and minimize economic impact on the poultry industry. [ABSTRACT FROM AUTHOR]

We present dynamical simulations and simple mechanics arguments to propose a system of stacked blocks of square lattices of elastic spheres that can be used to decimate an incident impulse. Mass mismatch between adjacent blocks is accomplished by making the sphere radius in the upper block twice that of the lower block. The system decimates impact energies by converting the initial impulse into two solitary waves and then progressively into many smaller amplitude solitary waves. We also show that near perfect impact decimation capability can be realized with increased mass mismatch between adjacent blocks by creating sandwiched structures in which a block with smaller density spheres is surrounded on both sides with blocks of denser spheres. The proposed systems are expected to be scalable down to spheres of $$\sim $$ 100 nm and work for solid and hollow spheres. [ABSTRACT FROM AUTHOR]

A device for absorbing and storing short duration impulses in an initially uncompressed onedimensional granular chain is presented. Simply stated, short regions of sufficiently soft grains are embedded in a hard granular chain. These grains exhibit long-lived standing waves of predictable frequencies regardless of the timing of the arrival of solitary waves from the larger matrix. We explore the origins, symmetry, and energy content of the soft region and its vibrational modes. [ABSTRACT FROM AUTHOR]

A molecular dynamics study on the collisional dynamics of soft and sticky single face-centered cubic crystal nanoparticles is presented. The softness and stickiness of the nanoparticles are controlled by varying parameters in the Lennard-Jones potential that is used to describe the interatomic interactions. Softening of nanoparticles due to extensive plastic deformations is observed as was previously found in hard nanoparticles. Further, two primary plastic deformation modes, slip and twinning, of the nanoparticles are found to play important roles in the temperature dependence of the coefficient of restitution. Additionally, we observe the effects of surface roughness, facets, and edges in the collisional behaviors of the sticky nanoparticles in low-velocity collisions. Nevertheless, the Johnson-Kendall-Roberts theory for macroscopic adhesive bodies still remains valid in nearly spherical nanoparticles. [ABSTRACT FROM AUTHOR]

The segregation of binary mixtures in a filled rotating double-walled drum is explored by simulations. Based on the characteristics of self-gravity and the centrifugal force, we argue that both percolation and buoyancy effects dominate the segregation process. The simulational results show that up to long enough times the segregation state is controlled by the rotational speed, the particle radius and density. At low rotational speeds, the smaller and heavier particles tend to accumulate towards the inner drum wall and the bigger and lighter ones towards the outer drum wall, while the segregation pattern reverses completely at higher rotational speeds. Two typical phase diagrams in the space of the density and radius ratio of bigger particles to smaller particles further confirm the predictions. Graphical abstract: [ABSTRACT FROM AUTHOR]

We modify the formulation of Hertz contact theory between two elastic half-solids with axial symmetry and show that these modifications to Hertz's original framework allow the development of force laws of the form F∞zn, 10 to describe any aspect ratio in the two bodies, all being valid near the contact surface. We let the x-y plane be the contact surface with an averaged pressure across the same as opposed to a pressure profile that depends on the contact area of a nonconformal contact as originally used by Hertz. We let the z axis connect the centers of the masses and define z1,2=xβ/R1,2β-1+yβ/(mR1,2)β-1, where z1,2⩾0 refers to the compression of bodies 1, 2, β>1, m>0, x,y⩾0. The full cross section can be generated by appropriate reflections using the first quadrant part of the area. We show that the nonlinear repulsive force is F=azn, where n≡1+1/β, and z≡z1+z2 is the overlap and we present an expression for a=f(E,σ,m,β,R1,R2) with E and σ as Young's modulus and the Poisson ratio, respectively. For β=2,∞, to similar geometry-dependent constants, we recover Hertz's law and the linear law, describing the repulsion between compressed spheres and disks, respectively. The work provides a connection between the contact geometry and the nonlinear repulsive law via β and m. [ABSTRACT FROM AUTHOR]

We introduce a novel agent based model where each agent carries an effective viral load that captures the instantaneous state of infection of the agent. We simulate the spread of a pandemic and subsequently validate it by using publicly available COVID-19 data. Our simulation tracks the temporal evolution of a virtual city or community of agents in terms of contracting infection, recovering asymptomatically, or getting hospitalized. The virtual community is divided into family groups with 2–6 individuals in each group. Agents interact with other agents in virtual public places like at grocery stores, on public transportation and in offices. We initially seed the virtual community with a very small number of infected individuals and then monitor the disease spread and hospitalization over a period of fifty days, which is a reasonable time-frame for the initial spread of a pandemic. An uninfected or asymptomatic agent is randomly selected from a random family group in each simulation step for visiting a random public space. Subsequently, an uninfected agent contracts infection if the public place is occupied by other infected agents. We have calibrated our simulation rounds according to the size of the population of the virtual community for simulating realistic exposure of agents to a contagion. Our simulation results are consistent with the publicly available hospitalization and ICU patient data from three distinct regions of varying sizes in New York state. Our model can predict the trend in epidemic spread and hospitalization from a set of simple parameters and could be potentially useful in predicting the disease evolution based on available data and observations about public behavior. Our simulations suggest that relaxing the social distancing measures may increase the hospitalization numbers by some 30% or more. [ABSTRACT FROM AUTHOR]

Inspired by partisan competitions and contentious elections in democratic countries, we numerically explore the effect of campaign strategies and related factors on the opinion of an electorate. The nature of the electorate is modeled through agents with different behaviors, such as, being conformist, contrarian or inflexible. The agents are assumed to take discrete opinion values that depend on both internal and external influences. The inhomogeneity of external influence on individuals is modeled as a random field. Two types of electorates have been considered. In an electorate with only conformist agents short-duration high impact campaigns are highly effective. These are, however, also sensitive to perturbations at the local level modeled as inflexibles and/or absentees. In electorates with both conformist and contrarian agents and varying level of dominance due to local factors, short-term campaigns are effective only in the case of fragile dominance of a single party. Strong local dominance is relatively difficult to influence and long term campaigns with strategies aimed to impact local level politics are seen to be more effective. • Sociophysics model with random field for partisan competition. • Mixed model with contrarian, conformist and inflexible agents. • Efficiency of campaigns and strategies for different levels of dominance. [ABSTRACT FROM AUTHOR]

We study the head-on collision of two solitary waves in a precompressed granular chain using the discrete element method. Our study takes the Toda chain solution as the initial condition for the simulations. The simulation covers the dynamical evolution of the collision process from the start of the incident wave to the end of the collision. The interaction has a central collision region of about five-grain width in which two solitary waves merge completely and share only one peak. Four stages, i.e., the pre-in-phase traveling stage, lag-phase collision state, lead-phase collision state, and post-in-phase traveling stage, are identified to describe the complex collision processes. Our results may be helpful for explaining the existence of long-lived solitary waves seen in the simulations by Takato and Sen [Europhys. Lett. 100 (2012) 24003]. [ABSTRACT FROM AUTHOR]

In this paper, we expand upon our recent studies of an agent-based model of a battle between an intelligent army and an insurgent army to explore the role of modifying strategy according to the state of the battle (adaptive strategy) on battle outcomes. This model leads to surprising complexity and rich possibilities in battle outcomes, especially in battles between two well-matched sides. We contend that the use of adaptive strategies may be effective in winning battles. [ABSTRACT FROM AUTHOR]

Abstract: We revisit the dynamical behavior of particles in a chain of spherical elastic grains, where the system is assumed to be placed in such a way that the grains suffer progressive loading as function of depth due to the presence of the gravitational acceleration . Here we address, for the first time, the dynamics of the surface grain in this rather well studied problem (see [R.S. Sinkovits, S. Sen, Phys. Rev. Lett. 74 (1995) 2686; J. Hong, J.Y. Ji, H. Kim, Phys. Rev. Lett. 82 (1999) 3058]) and make predictions that may be verified experimentally by monitoring the dynamics of a single edge grain. When , the surface grain dynamics can be associated with the problem of propagation of solitary waves in the chain. When , the dynamics of the surface grain turns out to be dramatically different, reflective of the very different dynamics exhibited by the grains in a gravitationally loaded chain. As we shall see, these studies provide a necessary first step towards developing an understanding of a difficult but important problem in physics and engineering — namely, the dynamics of the surface grains of a gravitationally loaded close-packed granular bed. [Copyright &y& Elsevier]

We present a study of the dynamics of a system of masses connected by springs and repelling by a 1 ∕ r potential in 1D. The present study focuses on the dynamics in the regime where the repulsive force dominates the dynamics of the system. We conjecture that such a system may be approximately modeled by an alignment of repelling rigid bar magnets that are sufficiently far apart from each other. We show that except for cases where the repulsive potential is very weak, most of the energy due to a velocity perturbation at system initiation of magnitude v 0 (0) generates a propagating solitary wave in the system. Dynamical simulations show that this solitary wave shows no measurable tendency to thermalize over extended simulation time scales, thereby yielding an effectively non-ergodic system. Part of the energy generates low-amplitude persistent oscillations which do not show any measurable interaction with the solitary wave. We find that the solitary wave propagation speed v S W ∝ v 0 2 for various coupling strengths. We further demonstrate that owing to the repulsion between the adjacent particles, these solitary waves are mutually repulsive, i.e., they cannot cross each other and hence there is no phase change associated with their mutual interactions. We use the data driven Dynamic Mode Decomposition technique to develop a simple approximate way to represent the propagating solitary wave. Additionally, we compute fluctuations in the kinetic energy of the system at late times and show that the energy fluctuations increase drastically when the effects of v 0 and the coupling associated with the repulsive interactions become competitive. • Highly unstable dynamical systems for wind and vibrational energy harvesting. • Solitons and solitary waves in magnetic chains. • Non ergodic and partly ergodic systems. • Dynamic mode decomposition study of solitons. [ABSTRACT FROM AUTHOR]

Purpose: To describe clinical course, characteristics, and outcome of reticular epithelial corneal edema (RECE) occurring as a not-so-infrequent adverse effect of a novel drug, Rho-kinase inhibitors (ROCK-I)- netarsudil (0.02%) and ripasudil (0.4%)., Methods: This was a retrospective observational non-randomized study. In this study, 12 eyes of 11 patients presenting at a tertiary eye care center between April 2021 and September 2021 were included. All 12 eyes developed a distinctive honeycomb pattern of RECE after starting topical ROCK-I. All patients were subjected to detailed ophthalmic examinations., Results: Eight patients were started on netarsudil (0.02%) and three on ripasudil (0.4%). Five eyes had a prior history of corneal edema. The remaining seven had the presence of ocular comorbidities predisposing to corneal edema. The average time for RECE occurrence was 25 days for netarsudil and 82 days for ripasudil. Visual acuity decreased in two eyes, remained unaffected in four eyes, and could not be quantified in four eyes due to preexisting profound visual impairment. Five eyes had symptoms of ocular surface discomfort associated with bullae. Symptoms and bullae resolved in all eyes in whom ROCK-I was stopped. The average time to resolution of RECE was 10 days for netarsudil and 25 days for ripasudil., Conclusion: RECE after ROCK-I occurs with the use of both netarsudil and ripasudil, although the characteristics differ. The presence of corneal edema and endothelial decompensation seem to be a risk factor, and cautious use is warranted in these patients. Four clinical stages of RECE are described. ROCK-I act as a double-edged sword in patients with endothelial decompensation. Large-scale studies are required to know the exact incidence, pathophysiology, and long-term consequences of the aforementioned side-effect., Competing Interests: None

We propose a granular architecture as a potential impact protector and signal filter. The system consists of monodispersed granular chains decorated with side beads fixed (welded) on sidewalls. Numerical results from usual monodispersed chains and simple tapered chains are employed as reference. An appropriate material combination and an optimal radii ratio between the side and axial granules show that more than 90% of the momentum amplitude of solitary pulses can be attenuated using a small and scalable system composed of five axial granules. Considering sinusoidal signals, the findings suggest that regular chains (monodispersed and tapered) are low-pass filters with cutoff frequencies as functions of the driven amplitude, restitutional losses, and tapering. The granular chain with fixed decoration filters all the input signals.

In this molecular dynamics study, we examine the local surface geometric effects of the normal impact force between two approximately spherical nanoparticles that collide in a vacuum. Three types of surface geometries-(i) crystal facets, (ii) sharp edges, and (iii) amorphous surfaces of small nanoparticles with radii R <10 nm-are considered. The impact forces are compared with their macroscopic counterparts described by nonlinear contact forces based on Hertz contact mechanics. In our simulations, edge and amorphous surface contacts with weak surface energy reveal that the average impact forces are in excellent agreement with the Hertz contact force. On the other hand, facet collisions show a linearly increasing force with increasing compression. Our results suggest that the nearly spherical nanoparticles are likely to enable some nonlinear dynamic phenomena, such as breathers and solitary waves observed in granular materials, both originating from the nonlinear contact force., Competing Interests: We declare we have no competing interests.

The microscopic basis of Newton's law of cooling and its modification when the difference in temperature between the system and the surroundings is very large is discussed. When the system of interest is interacting with a small bath, the effect of the dynamical evolution of the bath variables is important to find out its dynamical feedback on the system. As in the usual system-bath approach, however, the bath is finally considered to be in thermal equilibrium and thereby provides an effective generalization of the Born-Markov master equation. It is shown that the cooling at early time is faster than that predicted by Newton's law due to the dynamical feedback of the bath.

We report a particle dynamics based simulational study of the propagation of delta function mechanical impulses in idealized three-dimensional hexagonal close packed lattices of monosized Hertz spheres. This paper presents five key results on the kinetic energy of grains at the surface of a granular bed after the generation of a normal impulse into the bed. (i) We find that the time integrated or cumulative average kinetic energy per surface grain, kappa, drops as an impulse penetrates into the bed. The minimum value of kappa, say kappa(0), is reached at some time t=tau after the impulse has been generated. (ii) This value, kappa(0), depends upon the restitutional losses at the grain contacts and kappa(0) increases as restitutional losses at granular contacts increase in magnitude. (iii) The asymptotic value of kappa is denoted by kappa(final) . Our data show that increasing the area across which an impulse is generated, A, leads to kappa(final) proportional to A(-1/2) . (iv) If we assign random masses to our monosized grains, kappa(final) grows quadratically as a function of the range of mass variation about a mean mass. We find that at large times, i.e., t>>tau , kappa proportional to (1-exp [k (1-t/tau)]) , where the constant k is roughly independent of restitution for the typical values of restitution encountered. (v) Our data suggest that at early times, the backscattering process carries signatures of ballistic propagation of the mechanical energy while at late times, the backscattering process is reminiscent of vibrations of an essentially ergodic system. Given the ballisticlike propagation of mechanical energy into granular beds, we conclude that a wave equation based description of mechanical energy propagation into granular beds may not always be appropriate.