171 research outputs found
Jeans' gravitational instability and nonextensive kinetic theory
The concept of Jeans gravitational instability is rediscussed in the
framework of nonextensive statistics and its associated kinetic theory. A
simple analytical formula generalizing the Jeans criterion is derived by
assuming that the unperturbed self- gravitating collisionless gas is
kinetically described by the -parameterized class of power law velocity
distributions. It is found that the critical values of wavelength and mass
depend explicitly on the nonextensive -parameter. The standard Jeans
wavelength derived for a Maxwellian distribution is recovered in the limiting
case =1. For power-law distributions with cutoff, the instability condition
is weakened with the system becoming unstable even for wavelengths of the
disturbance smaller than the standard Jeans length .Comment: 5 pages, including 3 figures. Accepted for publication in A&
Higher Order Methods for Simulations on Quantum Computers
To efficiently implement many-qubit gates for use in quantum simulations on
quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2
+ ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2
\Delta t], ... which is accurate to 3rd or 4th order in \Delta t. The methods
we derive are an extended form of symplectic method and can also be used for
the integration of classical Hamiltonians on classical computers. We derive
both integral and irrational methods, and find the most efficient methods in
both cases.Comment: 21 pages, Latex, one figur
Transport coefficients and nonextensive statistics
We discuss the basic transport phenomena in gases and plasmas obeying the
-nonextensive velocity distribution (power-law). Analytical expressions for
the thermal conductivity () and viscosity () are derived by
solving the Boltzmann equation in the relaxation-time approximation. The
available experimental results to the ratio {}/ constrains the
-parameter on the interval . In the extensive limiting
case, the standard transport coefficients based on the local Gaussian
distribution are recovered, and due to a surprising cancellation, the electric
conductivity of a neutral plasma is not modified.Comment: 14 pages, 3 figures, REVTEX, submitted to PR
Renormalized Equilibria of a Schloegl Model Lattice Gas
A lattice gas model for Schloegl's second chemical reaction is described and
analyzed. Because the lattice gas does not obey a semi-detailed-balance
condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent
set of equations for the exact homogeneous equilibria are described, using a
generalized cluster-expansion scheme. These equations are solved in the
two-particle BBGKY approximation, and the results are compared to numerical
experiment. It is found that this approximation describes the equilibria far
more accurately than the Boltzmann approximation. It is also found, however,
that spurious solutions to the equilibrium equations appear which can only be
removed by including effects due to three-particle correlations.Comment: 21 pages, REVTe
A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
We describe a new polynomial time quantum algorithm that uses the quantum
fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian
operator, and that can be applied in cases (commonly found in ab initio physics
and chemistry problems) for which all known classical algorithms require
exponential time. Applications of the algorithm to specific problems are
considered, and we find that classically intractable and interesting problems
from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page
Correlations and Renormalization in Lattice Gases
A complete formulation is given of an exact kinetic theory for lattice gases.
This kinetic theory makes possible the calculation of corrections to the usual
Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of
correlations. It is shown that renormalized transport coefficients can be
calculated perturbatively by summing terms in an infinite series. A
diagrammatic notation for the terms in this series is given, in analogy with
the diagrammatic expansions of continuum kinetic theory and quantum field
theory. A closed-form expression for the coefficients associated with the
vertices of these diagrams is given. This method is applied to several standard
lattice gases, and the results are shown to correctly predict experimentally
observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure
Recommended from our members
Identifying Spatial Variability in Greenland’s Outlet Glacier Response to Ocean Heat
Although the Greenland ice sheet is losing mass as a whole, patterns of change on both local and regional scales are complex. Spatial statistics reveal large spatial variability of dynamic thinning rates of Greenland’s marine-terminating glaciers between 2003 and 2009; only 18% of glacier thinning rates co-vary with neighboring glaciers. Most spatially-correlated thinning rates are clusters of stable glaciers in the Thule, Scoresby Sund, and Southwest regions. Conversely, where spatial-autocorrelation is low, individual glaciers are more strongly controlled by local, glacier-scale features than by regional influences. We investigate possible sources of local control of oceanic forcing by combining grounding line depths and ocean model output to estimate mean ocean heat content adjacent to 74 glaciers. Linear regression models indicate stronger correlation of dynamic thinning rates with ocean heat content compared to those with grounding line depths alone. The correlation between ocean heat and dynamic thinning is robust for all of Greenland except glaciers in the West, and strongest in the Southeast (R2 ∼ 0.81 ± 0.15, ρ = 0.009), implying that glaciers with deeper grounded termini here are most sensitive to changes in ocean forcing. In the Northwest, accounting for shallow sills in the regressions improves the correlation of water depth with glacial thinning, highlighting the need for comprehensive knowledge of fjord geometry
Nonextensive Thermostatistics and the H-Theorem
The kinetic foundations of Tsallis' nonextensive thermostatistics are
investigated through Boltzmann's transport equation approach. Our analysis
follows from a nonextensive generalization of the ``molecular chaos
hypothesis". For , the -transport equation satisfies an -theorem
based on Tsallis entropy. It is also proved that the collisional equilibrium is
given by Tsallis' -nonextensive velocity distribution.Comment: 4 pages, no figures, corrected some typo
Computer simulations of domain growth and phase separation in two-dimensional binary immiscible fluids using dissipative particle dynamics
We investigate the dynamical behavior of binary fluid systems in two
dimensions using dissipative particle dynamics. We find that following a
symmetric quench the domain size R(t) grows with time t according to two
distinct algebraic laws R(t) = t^n: at early times n = 1/2, while for later
times n = 2/3. Following an asymmetric quench we observe only n = 1/2, and if
momentum conservation is violated we see n = 1/3 at early times. Bubble
simulations confirm the existence of a finite surface tension and the validity
of Laplace's law. Our results are compared with similar simulations which have
been performed previously using molecular dynamics, lattice-gas and
lattice-Boltzmann automata, and Langevin dynamics. We conclude that dissipative
particle dynamics is a promising method for simulating fluid properties in such
systems.Comment: RevTeX; 22 pages, 5 low-resolution figures. For full-resolution
figures, connect to http://www.tcm.phy.cam.ac.uk/~ken21/tension/tension.htm
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