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Auditya Sharma - One of the best experts on this subject based on the ideXlab platform.
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susceptibilities for the muller hartmann zitartz Countable Infinity of phase transitions on a cayley tree
Physical Review E, 2015Co-Authors: Auditya SharmaAbstract:We obtain explicit susceptibilities for the Countable Infinity of phase transition temperatures of Muller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to Infinity below it.
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order parameters for the muller hartmann zitartz Countable Infinity of phase transitions on a cayley tree
2015Co-Authors: Auditya SharmaAbstract:We obtain explicit susceptibilities for the Countable Infinity of phase transition temperatures of Muller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to Infinity below it.
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susceptibilities for the m uller hartmann zitartz Countable Infinity of phase transitions on a cayley tree
arXiv: Statistical Mechanics, 2015Co-Authors: Auditya SharmaAbstract:We obtain explicit susceptibilities for the Countable Infinity of phase transition temperatures of M\"{u}ller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to Infinity below it.
Zgliczyński Piotr - One of the best experts on this subject based on the ideXlab platform.
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A geometric method for infinite-dimensional chaos : symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
'Elsevier BV', 2020Co-Authors: Wilczak Daniel, Zgliczyński PiotrAbstract:We propose a general framework for proving that a compact, infinite-dimensional map has an invariant set on which the dynamics is semiconjugated to a subshift of finite type. The method is then applied to certain Poincaré map of the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter . We give a computer-assisted proof of the existence of symbolic dynamics and Countable Infinity of periodic orbits with arbitrary large periods
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Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line --- a computer-assisted proof
2017Co-Authors: Wilczak Daniel, Zgliczyński PiotrAbstract:The Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter $\nu=0.1212$ is considered. We give a computer-assisted proof the existence of symbolic dynamics and Countable Infinity of periodic orbits with arbitrary large periods.Comment: 40 pages, 7 figure
Alexander F Vakakis - One of the best experts on this subject based on the ideXlab platform.
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new family of solitary waves in granular dimer chains with no precompression
Physical Review E, 2011Co-Authors: K R Jayaprakash, Yuli Starosvetsky, Alexander F VakakisAbstract:In the present paper we report the existence of a new family of solitary waves in general one-dimensional dimer chains with elastic interactions between beads obeying a strongly nonlinear Hertzian force law. These dimers consist of pairs of ``heavy'' and ``light'' beads with no precompression. The solitary waves reported herein can be considered as analogous to the solitary waves in general homogeneous granular chains studied by Nesterenko, in the sense that they do not involve separations between beads, but rather satisfy special symmetries or, equivalently antiresonances in their intrinsic dynamics. We conjecture that these solitary waves are the direct products of a Countable Infinity of antiresonances in the dimer. An interesting finding is that the solitary waves in the dimer propagate faster than solitary waves in the corresponding homogeneous granular chain obtained in the limit of no mass mismatch between beads (i.e., composed of only heavy beads). This finding, which might seem counterintuitive, indicates that under certain conditions nonlinear antiresonances can increase the speed of disturbance transmission in periodic granular media, through the generation of different ways for transferring energy to the far field of these media. From a practical point of view, this result can have interesting implications in applications where granular media are employed as shock transmitters or attenuators.
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complex dynamics and targeted energy transfer in linear oscillators coupled to multi degree of freedom essentially nonlinear attachments
Nonlinear Dynamics, 2007Co-Authors: Stylianos Tsakirtzis, Alexander F Vakakis, Panagiotis Panagopoulos, Gaetan Kerschen, O V Gendelman, Lawrence A BergmanAbstract:We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of Countable Infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency–energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers.
Remick Kevin - One of the best experts on this subject based on the ideXlab platform.
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Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results
'ASME International', 2013Co-Authors: Remick Kevin, Vakakis Alexander, Michael Mcfarland, Quinn D. Dane, Sapsis, Themistoklic P.Abstract:This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a Countable Infinity of periodic orbits and an unCountable Infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results
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Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results
'ASME International', 2013Co-Authors: Remick Kevin, Vakakis Alexander, Quinn D. Dane, Mcfarland D. Michael, Sapsis ThemistoklisAbstract:This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a Countable Infinity of periodic orbits and an unCountable Infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results.National Science Foundation (U.S.) (Grant CMMI-1100722
Wilczak Daniel - One of the best experts on this subject based on the ideXlab platform.
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A geometric method for infinite-dimensional chaos : symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
'Elsevier BV', 2020Co-Authors: Wilczak Daniel, Zgliczyński PiotrAbstract:We propose a general framework for proving that a compact, infinite-dimensional map has an invariant set on which the dynamics is semiconjugated to a subshift of finite type. The method is then applied to certain Poincaré map of the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter . We give a computer-assisted proof of the existence of symbolic dynamics and Countable Infinity of periodic orbits with arbitrary large periods
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Symbolic dynamics for Kuramoto-Sivashinsky PDE on the line --- a computer-assisted proof
2017Co-Authors: Wilczak Daniel, Zgliczyński PiotrAbstract:The Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter $\nu=0.1212$ is considered. We give a computer-assisted proof the existence of symbolic dynamics and Countable Infinity of periodic orbits with arbitrary large periods.Comment: 40 pages, 7 figure
