Krishna Mohan Thamattoor - Academia.edu (original) (raw)

Papers by Krishna Mohan Thamattoor

arXiv (Cornell University), Oct 20, 2005

We recently introduced a simple toy model to describe energy propagation and backscattering in co... more We recently introduced a simple toy model to describe energy propagation and backscattering in complex layered media (T.R. Krishna Mohan and S. Sen, Phys. Rev. E 67, 060301(R) (2003)). The model provides good qualitative description of energy propagation and backscattering in real soils. Here we present a dynamical study of energy propagation and backscattering in a gravitationally loaded granular chain and compare our results with those obtained using the toy model. The propagation is ballistic for low g values and acquires characteristics of acoustic propagation as g is increased. We focus on the dynamics of the surface grain and examine the backscattered energy at the surface. As we shall see, excellent agreement between the two models is achieved when we consider the simultaneous presence of acoustic and nonlinear behavior in the toy model. Our study serves as a first step towards using the toy model to describe impulse propagation in gravitationally loaded soils.

We study a simple 1D model of dust rods, with mean size \mu, passing through a parallel 1D alignm... more We study a simple 1D model of dust rods, with mean size \mu, passing through a parallel 1D alignment of pores as a problem of clogging of a filter by dust grains; \mu is kept less than the pore size, s. We assume that the filter is "sticky", characterized by some parameter 0 \le \lambda \le 1, which means that dust grains slightly smaller in size than s can get trapped in the pores. Our analyses suggest that the number of clogged pores, N_{cl}, grows in time as t_N^{clog} \propto N_{cl}^{\nu}, where \nu = \nu(\mu,\lambda) is a non-universal exponent that depends upon the dust size distribution and filter properties.

International Journal of Modern Physics B, 2005

Mechanical energy, such as sound waves and impulses, have been used to detect shallow buried obje... more Mechanical energy, such as sound waves and impulses, have been used to detect shallow buried objects for more than half a century. Yet, very little is understood about how mechanical energy propagates into one of the simplest kinds of soil, namely, a granular bed. Here we present an overview of the state of the art in our understanding of mechanical energy propagation in granular beds.

International Journal of Modern Physics E, 2008

Multiple sclerosis (MS) is a chronic disabling disease of the central nervous system (CNS) that i... more 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.

MRS Proceedings, 2002

We discuss our recent work on simulational studies of impulse propagation and backscattering for ... more We discuss our recent work on simulational studies of impulse propagation and backscattering for the detection and imaging of shallow buried objects in close packed granular beds.

Physical Review E, 2014

We study the penetration dynamics of a projectile incident normally on a substrate comprising of ... more 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.

Physical Review E, 2003

Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclu... more Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires "cleaning up" of surface vibrations, and, in addition to 3D particle dynamics simulations, a phenomenological model to parameterize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters that allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed.

Sadhana, 1999

Pollution has reached levels which demand immediate attention and scientific and technological so... more Pollution has reached levels which demand immediate attention and scientific and technological solutions are required on an urgent basis. We are concerned in this paper with bioremediation of soil and groundwater, i.e. the use of indigenous micro-organisms to clean up soil beds and groundwater contaminated with organic pollutants. To achieve managedin situ bioremediation in practice, treated water is recycled with added nutrients into the ground so that oxygen and nitrogen are carried with the water to the subsurface regions. Sorption, convective-dispersive flow and chemical and biological transformations are the chief processes involved that have to be modelled. Here we discuss a simulation model developed to aid in designing an efficient system that maximizes the rate of biodegradation. Simulation models are a must in this case since laboratory experiments take time periods of the order of months. An unusual feature of this simulation model is that it is governed by coupled partial and ordinary differential equations. Partial differential equations (PDEs) model the diffusion and biodegradation processes occurring in the micropores of soil aggregates while ordinary differential equations (ODEs) describe the bioremediation in the interstitial spaces between soil aggregates, both partial and ordinary differential equations being nonlinear. The model is applied to the case of high initial contaminant concentrations.

Physical Review E, 2011

We quantify the correlation between earthquakes and use the same to distinguish between relevant ... more We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. Data pertaining to three different seismic regions, viz. California, Japan and Himalayas, are comparatively analyzed using such a network model. The distribution of recurrence lengths and recurrence times are two of the key features analyzed to draw conclusions about the universal aspects of such a network model. We find that the unimodal feature of recurrence length distribution, which helps to associate typical rupture lengths with different magnitude earthquakes, is robust across the different seismic regions. The out-degree of the networks shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws, with two regimes having different exponents, are obtained with recurrence time distribution. Thisis in agreement with the Omori law for aftershocks and extends it to spatial recurrences. The crossover to the second power law regime can be taken to be signalling the end of aftershock regime in an objective fashion.

Physical Review E, 2004

We report a particle dynamics based simulational study of the propagation of delta function mecha... more 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.

Physical Review E, 2009

The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the F... more 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. 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 have been known to be initiated by the quasi-static stretching of the bonds between the 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.

Physica D: Nonlinear Phenomena, 2007

We revisit the dynamical behavior of particles in a chain of spherical elastic grains, where the ... more 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 g. 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 g→0, the surface grain dynamics can be associated with the problem of propagation of solitary waves in the chain. When g>0, 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.

Physica A: Statistical Mechanics and its Applications, 2004

We consider 1D systems of masses, which can transfer energy via harmonic and/or anharmonic intera... more We consider 1D systems of masses, which can transfer energy via harmonic and/or anharmonic interactions of the form V (xi;i+1) ∼ x ÿ i; i+1 , where ÿ ¿ 2, and where the potential energy is physically meaningful. The systems are placed within boundaries or satisfy periodic boundary conditions. Any velocity perturbation in these (non-integrable) systems is found to travel as discrete solitary waves. These solitary waves very nearly preserve themselves and make tiny secondary solitary waves when they collide or reach a boundary. As time t → ∞, these systems cascade to an equilibrium-like state, with Boltzmann-like velocity distributions, yet with no equipartitioning of energy, which we refer to and brie y describe as the "quasi-equilibrium" state.

Journal of Seismology, 2010

We quantify the correlation between earthquakes and use the same to distinguish between relevant ... more We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws are also obtained with recurrence time distribution agreeing with the Omori law.

International Journal of Bifurcation and Chaos, 1998

Control mechanisms in the form of positive and negative feedback loops are responsible for the se... more Control mechanisms in the form of positive and negative feedback loops are responsible for the sensitivity and stability in the coherent behavior of the spatio-temporal organization in living cells. Models of these networks involving such feedback mechanisms have been shown to exhibit a rich spectrum of dynamical behaviors. A network involving both positive and negative feedbacks was earlier investigated by Sinha and Ramaswamy [1987]. We obtain a phase diagram of the possible dynamical behaviors for this model. Further, we investigate the origin and properties of the complex oscillations in the model. A simpler system is derived and shown to possess similar dynamical behaviors. Avenues for further investigation of the system with respect to relevant variations in some of the parameter values are suggested.

Computational and Mathematical Methods in Medicine, 2012

A simulation model for the spread and control of lesions in the brain is constructed using a plan... more A simulation model for the spread and control of lesions in the brain is constructed using a planar network (graph) representation for the central nervous system (CNS). The model is inspired by the lesion structures observed in the case of multiple sclerosis (MS), a chronic disease of the CNS. The initial lesion site is at the center of a unit square and spreads outwards based on the success rate in damaging edges (axons) of the network. The damaged edges send out alarm signals which, at appropriate intensity levels, generate programmed cell death. Depending on the extent and timing of the programmed cell death, the lesion may get controlled or aggravated akin to the control of wild fires by burning of peripheral vegetation. The parameter phase space of the model shows smooth transition from uncontrolled situation to controlled situation. The simulations show that the model is capable of generating a wide variety of lesion growth and arrest scenarios.

arXiv (Cornell University), Oct 20, 2005

We recently introduced a simple toy model to describe energy propagation and backscattering in co... more We recently introduced a simple toy model to describe energy propagation and backscattering in complex layered media (T.R. Krishna Mohan and S. Sen, Phys. Rev. E 67, 060301(R) (2003)). The model provides good qualitative description of energy propagation and backscattering in real soils. Here we present a dynamical study of energy propagation and backscattering in a gravitationally loaded granular chain and compare our results with those obtained using the toy model. The propagation is ballistic for low g values and acquires characteristics of acoustic propagation as g is increased. We focus on the dynamics of the surface grain and examine the backscattered energy at the surface. As we shall see, excellent agreement between the two models is achieved when we consider the simultaneous presence of acoustic and nonlinear behavior in the toy model. Our study serves as a first step towards using the toy model to describe impulse propagation in gravitationally loaded soils.

We study a simple 1D model of dust rods, with mean size \mu, passing through a parallel 1D alignm... more We study a simple 1D model of dust rods, with mean size \mu, passing through a parallel 1D alignment of pores as a problem of clogging of a filter by dust grains; \mu is kept less than the pore size, s. We assume that the filter is "sticky", characterized by some parameter 0 \le \lambda \le 1, which means that dust grains slightly smaller in size than s can get trapped in the pores. Our analyses suggest that the number of clogged pores, N_{cl}, grows in time as t_N^{clog} \propto N_{cl}^{\nu}, where \nu = \nu(\mu,\lambda) is a non-universal exponent that depends upon the dust size distribution and filter properties.

International Journal of Modern Physics B, 2005

Mechanical energy, such as sound waves and impulses, have been used to detect shallow buried obje... more Mechanical energy, such as sound waves and impulses, have been used to detect shallow buried objects for more than half a century. Yet, very little is understood about how mechanical energy propagates into one of the simplest kinds of soil, namely, a granular bed. Here we present an overview of the state of the art in our understanding of mechanical energy propagation in granular beds.

International Journal of Modern Physics E, 2008

Multiple sclerosis (MS) is a chronic disabling disease of the central nervous system (CNS) that i... more 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.

MRS Proceedings, 2002

We discuss our recent work on simulational studies of impulse propagation and backscattering for ... more We discuss our recent work on simulational studies of impulse propagation and backscattering for the detection and imaging of shallow buried objects in close packed granular beds.

Physical Review E, 2014

We study the penetration dynamics of a projectile incident normally on a substrate comprising of ... more 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.

Physical Review E, 2003

Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclu... more Impulses efficiently propagate into nominally dry granular beds and backscatter from buried inclusions in such beds may be potentially exploited to image shallow buried objects (SBOs). However, reliable imaging of SBOs requires "cleaning up" of surface vibrations, and, in addition to 3D particle dynamics simulations, a phenomenological model to parameterize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters that allows one to model surface vibrations, is consistent with experiments in a granular bed, and can help estimate the approximate signal transmission properties of the bed.

Sadhana, 1999

Pollution has reached levels which demand immediate attention and scientific and technological so... more Pollution has reached levels which demand immediate attention and scientific and technological solutions are required on an urgent basis. We are concerned in this paper with bioremediation of soil and groundwater, i.e. the use of indigenous micro-organisms to clean up soil beds and groundwater contaminated with organic pollutants. To achieve managedin situ bioremediation in practice, treated water is recycled with added nutrients into the ground so that oxygen and nitrogen are carried with the water to the subsurface regions. Sorption, convective-dispersive flow and chemical and biological transformations are the chief processes involved that have to be modelled. Here we discuss a simulation model developed to aid in designing an efficient system that maximizes the rate of biodegradation. Simulation models are a must in this case since laboratory experiments take time periods of the order of months. An unusual feature of this simulation model is that it is governed by coupled partial and ordinary differential equations. Partial differential equations (PDEs) model the diffusion and biodegradation processes occurring in the micropores of soil aggregates while ordinary differential equations (ODEs) describe the bioremediation in the interstitial spaces between soil aggregates, both partial and ordinary differential equations being nonlinear. The model is applied to the case of high initial contaminant concentrations.

Physical Review E, 2011

We quantify the correlation between earthquakes and use the same to distinguish between relevant ... more We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. Data pertaining to three different seismic regions, viz. California, Japan and Himalayas, are comparatively analyzed using such a network model. The distribution of recurrence lengths and recurrence times are two of the key features analyzed to draw conclusions about the universal aspects of such a network model. We find that the unimodal feature of recurrence length distribution, which helps to associate typical rupture lengths with different magnitude earthquakes, is robust across the different seismic regions. The out-degree of the networks shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws, with two regimes having different exponents, are obtained with recurrence time distribution. Thisis in agreement with the Omori law for aftershocks and extends it to spatial recurrences. The crossover to the second power law regime can be taken to be signalling the end of aftershock regime in an objective fashion.

Physical Review E, 2004

We report a particle dynamics based simulational study of the propagation of delta function mecha... more 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.

Physical Review E, 2009

The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the F... more 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. 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 have been known to be initiated by the quasi-static stretching of the bonds between the 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.

Physica D: Nonlinear Phenomena, 2007

We revisit the dynamical behavior of particles in a chain of spherical elastic grains, where the ... more 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 g. 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 g→0, the surface grain dynamics can be associated with the problem of propagation of solitary waves in the chain. When g>0, 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.

Physica A: Statistical Mechanics and its Applications, 2004

We consider 1D systems of masses, which can transfer energy via harmonic and/or anharmonic intera... more We consider 1D systems of masses, which can transfer energy via harmonic and/or anharmonic interactions of the form V (xi;i+1) ∼ x ÿ i; i+1 , where ÿ ¿ 2, and where the potential energy is physically meaningful. The systems are placed within boundaries or satisfy periodic boundary conditions. Any velocity perturbation in these (non-integrable) systems is found to travel as discrete solitary waves. These solitary waves very nearly preserve themselves and make tiny secondary solitary waves when they collide or reach a boundary. As time t → ∞, these systems cascade to an equilibrium-like state, with Boltzmann-like velocity distributions, yet with no equipartitioning of energy, which we refer to and brie y describe as the "quasi-equilibrium" state.

Journal of Seismology, 2010

We quantify the correlation between earthquakes and use the same to distinguish between relevant ... more We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws are also obtained with recurrence time distribution agreeing with the Omori law.

International Journal of Bifurcation and Chaos, 1998

Control mechanisms in the form of positive and negative feedback loops are responsible for the se... more Control mechanisms in the form of positive and negative feedback loops are responsible for the sensitivity and stability in the coherent behavior of the spatio-temporal organization in living cells. Models of these networks involving such feedback mechanisms have been shown to exhibit a rich spectrum of dynamical behaviors. A network involving both positive and negative feedbacks was earlier investigated by Sinha and Ramaswamy [1987]. We obtain a phase diagram of the possible dynamical behaviors for this model. Further, we investigate the origin and properties of the complex oscillations in the model. A simpler system is derived and shown to possess similar dynamical behaviors. Avenues for further investigation of the system with respect to relevant variations in some of the parameter values are suggested.

Computational and Mathematical Methods in Medicine, 2012

A simulation model for the spread and control of lesions in the brain is constructed using a plan... more A simulation model for the spread and control of lesions in the brain is constructed using a planar network (graph) representation for the central nervous system (CNS). The model is inspired by the lesion structures observed in the case of multiple sclerosis (MS), a chronic disease of the CNS. The initial lesion site is at the center of a unit square and spreads outwards based on the success rate in damaging edges (axons) of the network. The damaged edges send out alarm signals which, at appropriate intensity levels, generate programmed cell death. Depending on the extent and timing of the programmed cell death, the lesion may get controlled or aggravated akin to the control of wild fires by burning of peripheral vegetation. The parameter phase space of the model shows smooth transition from uncontrolled situation to controlled situation. The simulations show that the model is capable of generating a wide variety of lesion growth and arrest scenarios.