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After a review of the coupled Newton's equations for a small alignment of grains with a fixed reflecting end wall, the equations are put into block diagrams of Simulink. Simulink simulations are given for 6 grain systems for cubic and Hertz intergrain potentials. The expected granular solitary waves are seen in the simulations. The block diagrams hence convert a single impulse into a traveling energy bundle of fixed width. This work forms the necessary first step for the eventual realization of the mathematical system represented by the granular chain as a Very Large Scale Integrated (VLSI) circuit. © 2013 World Scientific Publishing Company.

World University root node

Department of Bioscience & Bioengineering

Modern Physics Letters B

Simulink modeling for circuit representation of granular chains

Kinetic energy fluctuations of a non-dissipative 1D granular chain held between perfectly reflecting walls with various precompressions are numerically investigated. The dynamics of the system is explored for three cases, i) for a weakly precompressed chain which admits only solitary waves that break down into secondary waves under wall collisions, which is consistent with other findings in the literature; ii) for a strongly precompressed chain which exhibits mostly acoustic waves; and iii) for a chain with intermediate precompression. Case iii) accommodates a nearly stable solitary wave that travels unaffected through the acoustic waves and bounces back and forth between the walls for extremely long times. © Copyright EPLA, 2012.

Long-lived solitary wave in a precompressed granular chain

Energy extraction from one source and perhaps in tandem from multiple natural sources such as wind, ocean waves and perhaps geothermal resources with devices that are not susceptible to wear and tear remains an outstanding challenge. Here we propose a simple, strongly non-linear system which is potentially capable of being tuned to just about any driving frequency and amplitude. The system consists of an alignment of N elastic spheres that are barely in contact and are of fixed or variable radius and held between two ends. When a persistent driving force is imparted at an edge grain, the system can end up in an oversqueezed state. Since a mechanical system must respond to unbalanced forces, such an oversqueezed system must eventually dilate. Persistent presence of the driving force can then end up forcing the system to vacillate between the oversqueezed and dilated states. The frequencies associated with such breathing processes are non-universal, depending on the system parameters and the details of the driving force itself This is why confined driven granular alignments can be made to respond to a wide range of frequencies and hence can turn out to be potentially useful tools for energy extraction. Here we briefly summarize our earlier work where we showed how these systems respond to a fixed driving force and then provide new results on the system response when time-dependent driving forces are involved. Needless to say, these systems may, in due course, be realized as both mechanical systems and as electrical circuits. © Authors 2011.

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Non-linear resonance-like processes in confined driven granular alignments and energy harvesting

The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam (FPU) and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced by the harmonic term stabilize the discrete breather by suppressing the breather's tendency to delocalize and disperse. We conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these systems. © Indian Academy of Sciences.

Pramana - Journal of Physics

Linearity stabilizes discrete breathers

Sustained ability to absorb impulses at varied temperatures using light, hard materials and at length scales of few centimeters has been a challenge. The tapered chains while effective have been difficult to construct for applications. Here we build on Hong's granular protector concept to show that strong inertial mismatches due to alternate sets of few massive and light grains in elastically matched monosized granular alignments seem promising in absorbing impulses across millisecond time scales within a few centimeters. We propose a system which could find applications in the context of the construction and automobile industries, in combat, and elsewhere. © 2011 American Institute of Physics.

Applied Physics Letters

Impulse absorption using small, hard panels of embedded cylinders with granular alignments

We introduce a stochastic model to study the problem of time evolution and outcome of simple two-party competitions or battles on a lattice where each party randomly deploys its constituents or elements to the lattice. The elements have assigned strength levels that determine how competitive or effective they are against the opponent. In our models, the elements neutralize one another when they are at the same site with a combination of strength levels and numbers determining which one gains control of the site. The competitions last until complete dominance has been established by one side by eliminating the opponents or a draw is achieved (unless the time evolution is terminated via some ad hoc condition). A Markov chain approach is used to describe the time-dependent dynamics of such competitions. The advantage of the approach is that it allows us to develop a theoretical framework for describing competitive systems where a combination of random and correlated events decide the outcome. We use the approach here for studies of highly contentious stochastic battles and for that of a battle with correlated events along with stochastic events. We present the method, a simple illustrative example on how the method works and close by considering two non-trivial cases including one with a combination of stochasticity and correlations. © 2011 Elsevier B.V. All rights reserved.

Physica A: Statistical Mechanics and its Applications

Dynamics of stochastic and nearly stochastic two-party competitions

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 Fzn, 1&lt;n&lt;∞, 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 R1 and R2 and invoke a factor m0 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 z 1,2=xα/R1,2α-1+yα/(mR1,2)α -1, where z1,2≥0 refers to the compression of bodies 1, 2, α1, m0, 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/α, and z=z 1+z2 is the overlap and we present an expression for a=f(E,σ,m,α,R1,R2) 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. © 2011 American Physical Society.

Fulltext

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Nonlinear repulsive force between two solids with axial symmetry

Defending a confined territory from a surprise attack is seldom possible. We use molecular dynamics and statistical physics inspired agent-based simulations to explore the evolution and outcome of such attacks. The study suggests robust emergent behavior, which emphasizes the importance of accurate surveillance, automated and powerful attack response, building layout, and sheds light on the role of communication restrictions in defending such territories. © 2011 World Scientific Publishing Company.

Agent based study of surprise attacks: Roles of surveillance, prompt reaction and intelligence

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. © 2011 American Physical Society.

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

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 × 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. © 2010 Kim et al; licensee BioMed Central Ltd.

BMC Infectious Diseases

Multi-agent modeling of the South Korean avian influenza epidemic

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. © 2009 The American Physical Society.

How solitary waves collide in discrete granular alignments

We study the nucleation, spreading, and control of irreversible diffusive damage in a 2D fixed-radius random network. The control is achieved via strategic self-destruction. Our studies suggest that rapidly activated aggressive and encompassing self-destruction may provide optimum long-term survival of the network. When the damaged area is sufficiently small, strategic self-destruction may be too dependent on local geometry and the details of the dynamics and hence non-trivial to estimate. Our results reveal broad insights into how it may be possible to combat and control the spreading of problematic effects across fixed-radius random networks. Copyright © EPLA, 2009.

Damage isolation via strategic self-destruction: A case study in 2D random networks

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. © 2009 The American Physical Society.

Dynamics of metastable breathers in nonlinear chains in acoustic vacuum

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 Ti6Al4 V, 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. © 2009 American Institute of Physics.

Journal of Applied Physics

Energy partitioning and impulse dispersion in the decorated, tapered, strongly nonlinear granular alignment: A system with many potential applications

A compressive applied force at the zero frequency limit applied on confined granular alignments is shown to result in tunable and higher frequency nonlinear granular breathing. We use extensive dynamical simulations and simple arguments to probe the origins of these breathing processes. In the presence of dissipation, the breathing has a lifetime that is inversely proportional to the dissipation constant. The possible use of the concept of nonlinear granular breathing in recovering the energy released at the beaches by surface gravity waves using a system made largely of nonmoving parts is mentioned as a possible application. © 2009 American Institute of Physics.

Nonlinear breathing processes in granular alignments

We consider a simple problem that of a horizontal alignment of identical grains, and insure that the grains are in gentle mutual contact and held between two rigid fixed end walls. Grain-grain interactions are intrinsically nonlinear according to the Hertz law and hence no sound waves can propagate through this alignment. The discussions here concern the solitary wave nature of propagation of any perturbation and its subsequent dispersion in the same vein as we probe the dispersion of a perturbation in linear response theory in statistical physics. We show that a perturbed granular alignment exhibits both decaying and growing solitary waves and can indeed reach an equilibrium-like state. We suggest that this equilibrium-like state may not be the equilibrium state commonly reached in thermodynamics and statistical physics. Moving beyond the effort to develop a deeper understanding of the energy transport problem in granular systems, we discuss a new application of a granular alignment system, that of driven granular alignments that show rich nonlinear dynamics and can turn out to be technologically meaningful entities. © 2009 American Institute of Physics.

AIP Conference Proceedings

Nonlinear, statistical and applied physics of solitary wavelike objects in granular systems

This research presents a multi agent model to estimate and predict the spread of Avian Influenza (AI) in various attributes and environments in a given population. AI can be transmitted by air and is a critical hazard to birds, especially chickens and ducks. The virus occurs naturally in birds and is capable of being transmitted from an infected bird to another. It is conceivable that AI could be a major threat to human health if the virus becomes capable of transmission to human beings. The next outbreak of AI could lead to millions of deaths unless a feasible strategy for AI containment can be developed. This paper focuses the flexibility that a multi agent system offers. Agent-based models can closely mimic the situations that exist in real system where several autonomous components may be interacting with each other. The modeling approach offers the advantage of examining the interactions between the agents. This research studies the interactions of three critical factors that characterize AI outbreaks. These properties are quarantine range, incubation period and infection probability. The multi agent model investigates the nature of spreading of AI by incorporating these three properties. We illustrate the potential benefits of multi agent modeling in containing the spreading of AI by presenting how efficiently the virus can be contained. Our work exploits data on the 2008 outbreak of AI in South Korea. © 2008 IEEE.

Proceedings - IEEE International Conference on Bioinformatics and Biomedicine, BIBM 2008

Multi-agent model analysis of the containment strategy for Avian Influenza (AI) in South Korea

Multiple sclerosis (MS) is a chronic disabling disease of the central nervous system (CNS) that is characterized by lesions with inflammatory cells, axons with the insulating myelin sheath damaged, and axonal loss. The causes of MS are not known and there is as yet no cure. The purpose of this research was to evaluate a physically motivated network model for lesion formation in the brain. The parsimonious network model contained two elements: (i) a spatially spreading pathological process causing cell damage and death leading to neuro-degeneration and, (ii) generation of alarm signals by the damaged cells that lead to activation of programmed death of cells surrounding the lesions in an attempt to contain the spatial spread of the pathologic process. Simulation results with a range of network geometries indicated that the model was capable of describing lesion progression and arrest. The modeling results also demonstrated dynamical complexity with sensitivity to initial conditions. © 2008 World Scientific Publishing Company.

International Journal of Modern Physics E

A computational model for lesion dynamics in multiple sclerosis of the brain

Solitary waves are lumps of energy. We consider the study of dynamical solitary waves, meaning cases where the energy lumps are moving, as opposed to topological solitary waves where the lumps may be static. Solitary waves have been studied in some form or the other for nearly 450 years. Subsequently, there have been many authoritative works on solitary waves. Nevertheless, some of the most recent studies reveal that these peculiar objects are far more complex than what we might have given them credit for. In this review, we introduce the physics of solitary waves in alignments of elastic beads, such as glass beads or stainless steel beads. We show that any impulse propagates as a new kind of highly interactive solitary wave through such an alignment and that the existence of these waves seems to present a need to re-examine the very definition of the concept of equilibrium. We further discuss the possibility of exploiting nonlinear properties of granular alignments to develop exciting technological applications. © 2008 Elsevier B.V. All rights reserved.

Physics Reports

Solitary waves in the granular chain

We propose that a battle between two conflicting entities can be modeled as a kinematic problem on a lattice. We examine the parameters relevant to such simulations, and describe global patterns emerging from a lattice model of a conflict with a few simple rules. We conclude that models of this type display interesting and relevant properties and warrant more in-depth analysis. The focus in this work is on the role of knowledge of the "neighborhood" in winning a battle. © 2008 World Scientific Publishing Company.