Reticular epithelial corneal edema as a novel side-effect of Rho Kinase Inhibitors: An Indian scenario.

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.

An agent-based model of spread of a pandemic with validation using COVID-19 data from New York State.

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.

Granular chains with fixed side decoration as impact protector and signals filter.

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.

Interactions of solitary waves in integrable and nonintegrable lattices.

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.

Small nanoparticles, surface geometry and contact forces.

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.

Fluctuations in Hertz chains at equilibrium.

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.

Rich collision dynamics of soft and sticky crystalline nanoparticles: numerical experiments.

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.

Granular chains with soft boundaries: Slowing the transition to quasiequilibrium.

We present here a detailed numerical study of the dynamical behavior of "soft" uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the formation of solitary waves (SWs). Here, however, the system response to the material properties of the grains and boundaries is explored further. In particular, we examine the details of the transition of the system from a SW phase to an equilibrium-like (or quasiequilibrium) phase, and for this reason we ignore the effects of dissipation in this study. We find that the soft walls slow the reflection of SWs at the boundaries of the system, which in turn slows the journey to quasiequilibrium. Moreover, the increased grain-wall compression as the boundaries are softened results in fewer average grain-grain contacts at any given time in the quasiequilibrium phase. These effects lead to increased kinetic energy fluctuations in the short term in softer systems. We conclude with a toy model that exploits the results of soft-wall systems. This toy model supports the formation of breather-like entities and may therefore be useful for localizing energy in desired places in the granular chain.

Solitary wave propagation through two-dimensional treelike structures.

It is well known that a velocity perturbation can travel through a mass spring chain with strongly nonlinear interactions as a solitary and antisolitary wave pair. In recent years, nonlinear wave propagation in 2D structures have also been explored. Here we first consider the propagation of such a velocity perturbation for cases where the system has a 2D "Y"-shaped structure. Here each of the three pieces that make up the "Y" are made of a small mass spring chain. In addition, we consider a case where multiple "Y"-shaped structures are used to generate a "tree." We explore the early time dynamical behavior associated with the propagation of a velocity perturbation initiated at the trunk and at the extremities for both cases. We are looking for the energy transmission properties from one branch to another of these "Y"-shaped structures. Our dynamical simulations suggest the following broad observations: (i) for strongly nonlinear interactions, mechanical energy propagation resembles pulse propagation with the energy propagation being dispersive in the linear case; (ii) for strong nonlinear interactions, the tree-like structure acts as an energy gate showing preference for large perturbations in the system while the behavior of the linear case shows no such preference, thereby suggesting that such structures can possibly act as switches that activate at sufficiently high energies. The study aspires to develop insights into the nature of nonlinear wave propagation through a network of linear chains.

Mechanical energy fluctuations in granular chains: the possibility of rogue fluctuations or waves.

The existence of rogue or freak waves in the ocean has been known for some time. They have been reported in the context of optical lattices and the financial market. We ask whether such waves are generic to late time behavior in nonlinear systems. In that vein, we examine the dynamics of an alignment of spherical elastic beads held within fixed, rigid walls at zero precompression when they are subjected to sufficiently rich initial conditions. Here we define such waves generically as unusually large energy fluctuations that sustain for short periods of time. Our simulations suggest that such unusually large fluctuations ("hot spots") and occasional series of such fluctuations through space and time ("rogue fluctuations") are likely to exist in the late time dynamics of the granular chain system at zero dissipation. We show that while hot spots are common in late time evolution, rogue fluctuations are seen in purely nonlinear systems (i.e., no precompression) at late enough times. We next show that the number of such fluctuations grows exponentially with increasing nonlinearity whereas rogue fluctuations decrease superexponentially with increasing precompression. Dissipation-free granular alignment systems may be possible to realize as integrated circuits and hence our observations may potentially be testable in the laboratory.

Granular chain between asymmetric boundaries and the quasiequilibrium state.

Some 30 years have passed since we learned that any velocity perturbation develops into a propagating solitary wave in a granular chain, and over a decade has passed since we learned that these solitary waves break and reform upon collision, leaving behind small secondary solitary waves. The production of the latter eventually precipitates the quasiequilibrium state characterized by large energy fluctuations in dissipation-free granular systems. Here we present dynamical simulations on the effects of soft boundaries on solitary wave interaction in granular chains held between fixed walls. We show that at short time scales, a gradient in the distribution of kinetic energy between the boundaries is indeed sustained. At long times, however, such a gradient gets obliterated and there is no measurable difference between the average kinetic energies of the particles adjacent to walls. Our findings suggest that (i) the quasiequilibrium state can effectively erase small gradients of the average kinetic energies of the particles adjacent to walls in a system, (ii) Boltzmann distribution of grain speeds is realized in the system of interest, and (iii) time and space averages yield the same result, thus suggesting that the system is ergodic.

Strong plastic deformation and softening of fast colliding nanoparticles.

Nanoparticles, with sizes ranging between 1 and ∼102 nm, show dynamical properties distinctly different than those of bulk materials. Due to their large surface area to volume ratio, their properties often depend on length scales. We investigate the size and the collision velocity (vcoll) dependence of the coefficient of restitution (COR) for nanoparticles made of a face-centered cubic lattice of Lennard-Jones atoms via nonequilibrium molecular dynamics simulations. A sharp crossover between elastic collision and plastic collision occurs when vcoll=vY, where vY is the size-dependent yield velocity. For high-collision velocities the COR ∼vcoll-α, α∼1. This result is in agreement with recent small system simulations and with experiments and is distinct from the elasticity-theory-based result for COR for inelastic collisions which behaves as vcoll-α, with α=14. We find that the size-dependent critical vY approaches the theoretical constant value for macroscopic spheres as our particle sizes grow. Possible insights into the origins of α∼1 and the size dependence of the yield velocity are suggested. The work also suggests that sufficiently fast moving nanoparticles traveling through vacuum could be sticky and hence could be of potential interest in many applications.

Drag-force regimes in granular impact.

We study the penetration dynamics of a projectile incident normally on a substrate comprising of smaller granular particles in three-dimensions using the discrete element method. Scaling of the penetration depth is consistent with experimental observations for small velocity impacts. Our studies are consistent with the observation that the normal or drag force experienced by the penetrating grain obeys the generalized Poncelet law, which has been extensively invoked in understanding the drag force in the recent experimental data. We find that the normal force experienced by the projectile consists of position and kinetic-energy-dependent pieces. Three different penetration regimes are identified in our studies for low-impact velocities. The first two regimes are observed immediately after the impact and in the early penetration stage, respectively, during which the drag force is seen to depend on the kinetic energy. The depth dependence of the drag force becomes significant in the third regime when the projectile is moving slowly and is partially immersed in the substrate. These regimes relate to the different configurations of the bed: the initial loose surface packed state, fluidized bed below the region of impact, and the state after the crater formation commences.

Spin Brazil-nut effect and its reverse in a rotating double-walled drum.

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.

Sustained strong fluctuations in a nonlinear chain at acoustic vacuum: beyond equilibrium.

Here we consider dynamical problems as in linear response theory but for purely nonlinear systems where acoustic propagation is prohibited by the potential, e.g., the case of an alignment of elastic grains confined between walls. Our simulations suggest that in the absence of acoustic propagation, the system relaxes using only solitary waves and the eventual state does not resemble an equilibrium state. Further, the studies reveal that multiple perturbations could give rise to hot and cold spots in these systems. We first use particle dynamics based simulations to understand how one of the two unequal colliding solitary waves in the chain can gain energy. Specifically, we find that for head-on collisions the smaller wave gains energy, whereas when a more energetic wave overtakes a less energetic wave, the latter gains energy. The balance between the rate at which the solitary waves break down and the rate at which they grow eventually makes it possible for the system to reach a peculiar equilibriumlike phase that is characteristic of these purely nonlinear systems. The study of the features and the robustness of the fluctuations in time has been addressed next. A particular characteristic of this equilibriumlike or quasiequilibrium phase is that very large energy fluctuations are possible--and by very large, we mean that the energy can vary between zero and several times the average energy per grain. We argue that the magnitude of the fluctuations depend on the nature of the nonlinearity in the potential energy function and the feature that any energy must eventually travel as a compact solitary wave in these systems where the solitary wave energies may vary widely. In closing we address whether these fluctuations are peculiar to one dimension or can exist in higher dimensions. The study hence raises the following intriguing possibility. Are there physical or biological systems where these kinds of nonlinear forces exist, and if so, can such large fluctuations actually be seen? Implications of the study are briefly discussed.

Nonlinear repulsive force between two solids with axial symmetry.

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 [Please see symbol] z(n), 1 < n < ∞, where F is the force and z is the distance between the centers of the two solids. The study suggests that it may be possible to design physical systems that can realize such force laws. We let the half-solids be characterized by radii of curvatures R(1) and R(2) and invoke a factor m>0 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 = x(α) / R(1,2)(α-1) + y(α)/(mR(1,2))(α-1), where z(1,2) ≥ 0 refers to the compression of bodies 1, 2, α > 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 = az(n), where n ≡ 1 + 1/α, and z ≡ z(1) + z(2) is the overlap and we present an expression for a = f(E, σ, m, α, R(1), R(2)) with E and σ as Young's modulus and the Poisson ratio, respectively. For α = 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 α and m.

Multi-agent modeling of the South Korean avian influenza epidemic.

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.

How solitary waves collide in discrete granular alignments.

Solitary waves in continuum media pass through each other with only a slight phase change. However, in an intrinsically nonlinear many-body system such solitary waves could behave differently. It was predicted and experimentally confirmed that head-on solitary wave collisions in granular alignments are followed by the formation of tiny secondary solitary waves in the vicinity of the collision point. While it remains a challenge to provide an analytical treatment of the local time evolution, we present arguments and associated simulations to address a crucial unknown, namely, why the secondary solitary waves must form. Extensive numerical investigations on solitary wave collisions at a grain center and at an edge show marked differences. The effects of softening the grain repulsion are discussed to validate the arguments.

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum.

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of "acoustic vacuum." Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are "fragile" in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

On the microscopic basis of Newton's law of cooling and beyond.

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.