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Full-Text Articles in Physical Sciences and Mathematics
Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, Jonathan Machta
Stationary States And Energy Cascades In Inelastic Gases, E. Ben-Naim, Jonathan Machta
Jonathan Machta
We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transferred from large velocity scales to small velocity scales. These steady states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v)∼v−σ. The exponent σ is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. …
Parallel Dynamics And Computational Complexity Of Network Growth Models, Benjamin Machta, Jonathan Machta
Parallel Dynamics And Computational Complexity Of Network Growth Models, Benjamin Machta, Jonathan Machta
Jonathan Machta
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a power α of the connectivity of the existing node. Algorithms for generating growing networks very quickly in parallel are described and studied. The sublinear and superlinear cases require distinct algorithms. As a result, there is a discontinuous transition in the parallel complexity of sampling these networks corresponding to the discontinuous structural transition at α=1, where the networks become scale-free. For α>1, networks …
Power-Law Velocity Distributions In Granular Gases, E. Ben-Naim, B. Machta, Jonathan Machta
Power-Law Velocity Distributions In Granular Gases, E. Ben-Naim, B. Machta, Jonathan Machta
Jonathan Machta
The kinetic theory of granular gases is studied for spatially homogeneous systems. At large velocities, the equation governing the velocity distribution becomes linear, and it admits stationary solutions with a power-law tail, f(v)∼v−σ. This behavior holds in arbitrary dimension for arbitrary collision rates including both hard spheres and Maxwell molecules. Numerical simulations show that driven steady states with the same power-law tail can be realized by injecting energy into the system at very high energies. In one dimension, we also obtain self-similar time-dependent solutions where the velocities collapse to zero. At small velocities there is a steady state and a …
Ground States And Thermal States Of The Random Field Ising Model, Yong Wu, Jonathan Machta
Ground States And Thermal States Of The Random Field Ising Model, Yong Wu, Jonathan Machta
Jonathan Machta
The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random field and external field strength. Thermal states and thermodynamic properties are obtained for all temperatures using the Wang-Landau algorithm. The specific heat and susceptibility typically display sharp peaks in the critical region for large systems and strong disorder. These sharp peaks result from large domains flipping. For a given realization of disorder, ground states and thermal states near the critical line are found to be strongly correlated—a concrete manifestation of the zero temperature fixed point scenario.