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Most environments inhabited by living beings have dust. Much of that dust comes from the continuous flaking of our own skin and atmosphere borne particles of submicron size. Dust mites seem to play an important role in integrating fine scale dust, which they consume to grow, resulting in larger length scale dust. Dust continues to agglomerate and grow. Air filters are designed to remove dust and control dust agglomeration. We report a simple scaling law, based on kinematic simulations of dust filtration through a one dimensional idealized filter. The results reveal insights regarding how filters may clog in time. Our results may be of use to someone interested in designing customized air filters for optimum dust removal in an environment with a known dust distribution. Copyright © 2004 SAE International.

World University root node

Department of Bioscience & Bioengineering

SAE Technical Papers

Removing dust from confined air volumes - A toy model

The propagation of δ function mechanical impulses in idealized three-dimensional hexagonal close packed lattices of monosized Hertz sphere was investigated using particle dynamics based simulation. The kinetic energy behavior of grains at cumulative surface of a granular bed after the generation of a normal impulse into the bed was also analyzed. It was found that the cumulative average kinetic energy per surface grain, κ, decreased with the penetration of the impulse into the bed. The results show that the minimum value of κ depends upon restitutional losses at the grain contacts.

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

Impulse penetration into idealized granular beds: Behavior of cumulative surface kinetic energy

Water-soluble ferrofluids typically have ferrolluid grains ≤20 nm or so in diameter. We argue that one maybe able to use a single liquid coated ferrofluid grain as an "ink drop" of a hypothetical inkjet printer. Such line scale drops may not be best suited for the desktop inkjet printer but may find a niche in other applications such as in tagging commodities to be protected from easy counterfeiting. © 2004 by Marcel Dekker, Inc.

Journal of Dispersion Science and Technology

Nanoprinting with nanoparticles: Concept of a novel inkjet printer with possible applications in invisible tagging of objects

We consider the dynamical behavior of horizontal alignments of elastic grains placed within confining walls and placed under a constant acceleration that is applied at one end of the system. We show that these systems vibrate under such a compressive force. Certain universal properties of this vibration are mentioned. These systems may be useful in designing devices for filtering out mechanical noise. Copyright © 2004 SAE International.

Periodic dynamics in driven granular chain systems

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 three-dimensional (3D) particle dynamics simulations, a phenomenological model to parametrize the bed surface may be useful for field applications. We introduce a 1D mean-field-like toy model with two parameters, which 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. © 2003 The American Physical Society.

Fulltext

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Impulse backscattering in granular beds: Introducing a toy model

Shock absorption traditionally exploits visco-elastic devices, fluid viscous dampers and friction dampers, or "soft" materials. Recent work on impulse propagation in granular assemblies suggests that it may be possible to absorb shock waves using a different variety of shock absorbers and thus unlock the possibility of building structures that are significantly more shock absorbent than is currently possible, an issue of relevance to concerns of security. These new shock absorbers are composed of granular materials and exploit the nonlinear energy propagation properties in assemblies of granular materials. They have the potential to partially recover the energy of the absorbed shock waves for useful purposes, a property that might allow one to design devices to convert the incident energy to other useful forms. The basic physics of the "tapered chain shock absorber" is briefly discussed in this work.

Materials Research Society Symposium - Proceedings

Energy absorption and recovery in tapered granular chains: Small chains and low tapering

A two-parameter model to describe impulse backscattering at the surface of a granular assembly is proposed. The model is robust, and, at the same time, sensitive to changes in the distribution of p across the layers. The model qualitatively reproduces the time evolution of average energy of the surface grains of a complex, heterogeneous medium such as granular beds, following the generation of a normal impulse at the bed surface.

The impulse backscattering based detection and imaging of shallow buried objects was discussed. The analyses show that it is possible to use impulses to detect and image buried objects in granular beds. The simulations also suggest that the sensors used to detect backscattering data in granular beds must be able to gather time data at intervals of 10-4 seconds or less.

Impulse backscattering based detection and imaging of shallow buried objects

We consider a chain of monodisperse elastic grains of radius R where the grains are barely in contact. The grains repel upon contact via the Hertz-type potential, [formula presented] [formula presented] where [formula presented] is the grain-grain overlap, [formula presented] where [formula presented] denotes the displacement of grain i from its original equilibrium position. This being a computational study, we consider n to be arbitrary. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an impulse propagates as a solitary wave of fixed spatial extent, [formula presented] through a chain of grains. Here, we develop on a recent study by Manciu, Sen, and Hurd [Phys. Rev. E 63, 016614 (2001)] that shows that colliding solitary waves in the chains of interest spawn a well-defined hierarchy of multiple secondary solitary waves (SSWs) that carry ∼0.5% or less of the energy of the original solitary waves. We show that the emergence of SSWs is a complex process where nonlinear forces and the discreteness of the grains lead to the partitioning of the available energy into hierarchies of SSWs. The process of formation of SSWs involves length scales and time scales that are controlled by the strength of the nonlinearity in the system. To the best of our knowledge, there is no formal theory that describes the dynamics associated with the formation of SSWs. Calculations for cases where the Hertz-type potential can be symmetric in the overlap parameter δ, i.e., where δ can be both positive and negative, suggest that the formation of secondary solitary waves may be a fundamental property of certain discrete, nonlinear systems. © 2002 The American Physical Society.

Secondary solitary wave formation in systems with generalized Hertz interactions

Solutions to Newton's equations for particles in one-body potentials of form V1(xi) = ∑p A(i)2pxi2p, where p &gt; 0 and an integer, can be regarded as generators of infinite sequences of correlated frequencies {Ωm}. Simple nonlinear potentials can hence provide efficient ways of generating correlated information. Two-body potentials V2(xi - xj) can provide ways to communicate aspects of that information between the correlated frequency sequences. Temperature and noise can play a role in introducing a time scale across which the frequencies retain their identity. Introduction of explicit time dependence in the energy terms might be appropriate for constructing top down versions of toy models for the brain, something that is lacking at the present time. The richness of the nonlinear system along with the effects of heat baths, external noise and time dependence allows for the possibility of describing aging effects, processing of information "templates" in the brain and of the development of correlations between such "templates". In short, nonlinearity, interactions, noise effects and introduction of time-dependent energies might allow for the construction of "top-down" models of the brain with the eventual goal of possibly unifying the neurological, molecular biological, biochemical and psychiatric approaches toward studying the brain. © 2002 Elsevier Science B.V. All rights reserved.

Physica A: Statistical Mechanics and its Applications

Proposal for a nonlinear top-down toy model of the brain

The Mori-Lee treatment of linear response theory demonstrates that the Laplace transform of any relaxation function of a dynamical variable can be expressed as a continued fraction. For certain simple nonlinear systems, the continued fraction representation of the relaxation functions cannot be evaluated perturbatively. It turns out that many body systems with even a single on-site nonlinearity can dramatically alter the relaxation behavior in such systems. We argue that nonperturbative continued fractions in the Mori-Lee formalism are necessarily associated with systems that exhibit relaxation that is sensitive to the presence of nonlinearities. © 2002 Elsevier Science B.V. All rights reserved.

Relaxation in nonlinear systems, nonconvergent infinite continued fractions and sensitive relaxation processes

Physica A - Statistical Mechanics and its Applications: Preface

We report particle dynamics based studies of impulse propagation in a chain of elastic beads with dissipative contacts and with randomly distributed masses. The interaction between the beads is characterized by the potential V(δ)∼δn, δ ≥ 0 being grain overlap, n 〉 2 and at zero external loading, i.e., under conditions of "sonic vacuum" in which sound cannot propagate through the chain [J. Appl. Mech. Technol. Phys. 5 (1983) 733]. In the earlier work, we have confirmed the studies of Nesterenko and coworkers and have reported that impulses propagate as solitary waves in the system of interest in the absence of dissipation and disorder [Physica A 268 (1999) 644]. In the present study, we first discuss the effects of restitution and velocity dependent friction on the propagation of the impulse. We next report that the maximum energy Emax of the solitary wave as it propagates from a chain of monodisperse grains of mass m to a chain with masses m(1 +r(z)ε), where -1≤r(z)≤1 and ε=const. that measures the degree of randomness, decays with linear distance traveled z as exp(-αEz), αE∼ ε2+f(n), f(n) being some n dependent constant for 2 〈 n 〈 ∞. In monodisperse chains, the velocity of the solitary wave c∼Emax(n-2)/2n. In polydisperse chains, we show that the propagation speed of a non-dispersive solitary wave decays with distance as exp(-αcz), where αc = αE(n-2)/2n. © 2001 Elsevier Science B.V. All rights reserved.

Physica D: Nonlinear Phenomena

Impulse propagation in dissipative and disordered chains with power-law repulsive potentials

The canonical ensemble relaxation function of a particle in a symmetric anharmonic potential well in D = 1 is known to exhibit slow algebraic behavior [S. Sen, R. S. Sinkovits and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996); R. S. Sinkovits, S. Sen, J. C. Phillips, and S. Chakravarti, Phys. Rev. E 59, 6497 (1999)]. In the present work, we report a study of relaxation of a particle in symmetric and asymmetric quartic anharmonic potential wells of the form V(x,y) = 1/2 (x2 + Cy2) + 1/4 (x2 + Cy2)2 in D = 2. The relaxation in the above system is identical to that in D = 1 wells when C = 0 (since it is then a D = 1 system) and C = 1. However, for O &lt; C &lt; 1 and for C≫1, the frequencies associated with well dynamics are strongly affected and hence the power spectra are altered as a function of C Our calculations suggest that the exponents of the long-time tails associated with the relaxation processes are insensitive to D. In closing, we comment on the consequences of our analysis for the study of slow dynamics in interacting many-particle systems that are connected by harmonic springs with the individual particles in anharmonic potential wells. ©2001 The American Physical Society.

Relaxation of classical particles in two-dimensional anharmonic single-well potentials

The equation of motion for a bead in a chain of uncompressed elastic beads in contact that interact via the potential [Formula Presented] δ being overlap, supports solitary waves and does not accommodate sound propagation [V. Nesterenko, J. Appl. Mech. Tech. Phys. 5, 733 (1983)]. We present an iteratively exact solution to describe the solitary wave as a function of material parameters and a universal, infinite set of coefficients, which depend only on n. We compute any arbitrary number of coefficients to desired accuracy and show that only the first few coefficients of our solution significantly improves upon Nesterenko’s solution. The improved solution is a necessary step to develop a theoretical understanding of the formation of secondary solitary waves [M. Manciu, et al., Phys. Rev. E 63, 011614 (2001)]. © 2001 The American Physical Society.

Solitary wave dynamics in generalized Hertz chains: An improved solution of the equation of motion

The canonical ensemble relaxation function of a particle in a symmetric anharmonic potential well in D = 1 is known to exhibit slow algebraic behavior [S. Sen, R. S. Sinkovits and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996); R. S. Sinkovits, S. Sen, J. C. Phillips, and S. ChakravartiPhys. Rev. E 59, 6497 (1999)]. In the present work, we report a study of relaxation of a particle in symmetric and asymmetric quartic anharmonic potential wells of the form V(x,y)= 1/2(x2 + Cy2)+ 1/4 (x2+ Cy2)2 in D = 2. The relaxation in the above system is identical to that in D= 1 wells when C=0 (since it is then a D= 1 system) and C= 1. However, for 0 &lt;C&lt;1 and for C≫1, the frequencies associated with well dynamics are strongly affected and hence the power spectra are altered as a function of C. Our calculations suggest that the exponents of the long-time tails associated with the relaxation processes are insensitive to D. In closing, we comment on the consequences of our analysis for the study of slow dynamics in interacting many-particle systems that are connected by harmonic springs with the individual particles in anharmonic potential wells. ©2001 The American Physical Society.

The canonical ensemble relaxation function of a particle in a symmetric anharmonic potential well in [formula presented] is known to exhibit slow algebraic behavior [S. Sen, R. S. Sinkovits and S. Chakravarti, Phys. Rev. Lett. 77, 4855 (1996); R. S. Sinkovits, S. Sen, J. C. Phillips, and S. Chakravarti, Phys. Rev. E 59, 6497 (1999)]. In the present work, we report a study of relaxation of a particle in symmetric and asymmetric quartic anharmonic potential wells of the form [formula presented] in [formula presented] The relaxation in the above system is identical to that in [formula presented] wells when [formula presented] (since it is then a [formula presented] system) and [formula presented] However, for [formula presented] and for [formula presented] the frequencies associated with well dynamics are strongly affected and hence the power spectra are altered as a function of C. Our calculations suggest that the exponents of the long-time tails associated with the relaxation processes are insensitive to D. In closing, we comment on the consequences of our analysis for the study of slow dynamics in interacting many-particle systems that are connected by harmonic springs with the individual particles in anharmonic potential wells. © 2001 The American Physical Society.

We establish that weak impulses can be effectively used to detect and image buried objects in disordered granular beds. The image carries information about the approximate shape of the surface of the buried object and its approximate location. Impulse backscattering can serve as a powerful tool to detect and to image the identity of buried metallic and non-metallic objects. © 2001 SPIE · 0277-786X/01/$15.00.

Proceedings of SPIE - The International Society for Optical Engineering

Impulse backscattering based detection and imaging of buried objects in granular beds

The propagation of an impulse through a finite chain of monodisperse elastic beads was studied. The grain diameters progressively shrink in radius by a factor 'q' in a finite chain of elastic beads. The spatial symmetry of the solitary wave was destroyed due to the progressively shrink in radius. It was observed that the trailing part of the wave travelled progressively slower as comparative to the leading edge. It was shown that the shock waves can be thermalized by the construction of tapered chains.

Thermalizing an impulse

We consider a chain of elastic beads subjected to vanishingly weak loading conditions, i.e., the beads are barely in contact. The grains repel upon contact via the Hertz-type potential, (Formula presented) (Formula presented) where (Formula presented) δ being the grain–grain overlap. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an impulse propagates as a solitary wave of fixed spatial extent (dependent only upon n) through a chain of Hertzian beads and demonstrate, to our knowledge for the first time, that colliding solitary waves in the chain spawn a well-defined hierarchy of multiple secondary solitary waves, which is ∼ 0.5% of the energy of the original solitary waves. Our findings have interesting parallels with earlier observations by Rosenau and colleagues [P. Rosenau and J. M. Hyman, Phys. Rev. Lett. 70, 564 (1993); P. Rosenau, ibid. 73, 1737 (1994); Phys. Lett. A 211, 265 (1996)] regarding colliding compactons. To the best of our knowledge, there is no formal theory that describes the dynamics associated with the formation of secondary solitary waves. Calculations suggest that the formation of secondary solitary waves may be a fundamental property of certain discrete systems. © 2000 The American Physical Society.