3,193 research outputs found
Linearisable third order ordinary differential equations and generalised Sundman transformations
We calculate in detail the conditions which allow the most general third
order ordinary differential equation to be linearised in X'''(T)=0 under the
transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are
considered.Comment: 33 page
Generalized Semimagic Squares for Digital Halftoning
Completing Aronov et al.'s study on zero-discrepancy matrices for digital
halftoning, we determine all (m, n, k, l) for which it is possible to put mn
consecutive integers on an m-by-n board (with wrap-around) so that each k-by-l
region holds the same sum. For one of the cases where this is impossible, we
give a heuristic method to find a matrix with small discrepancy.Comment: 6 pages, 6 figure
A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution
We present a derivation of the Jarzynski identity and the Crooks fluctuation
theorem for systems governed by deterministic dynamics that conserves the
canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics,
Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a
relation between the heat absorbed by the system during the non-equilibrium
process and the Jacobian of the phase flow generated by the dynamics.Comment: 12 page
Euler buckling instability and enhanced current blockade in suspended single-electron transistors
Single-electron transistors embedded in a suspended nanobeam or carbon
nanotube may exhibit effects originating from the coupling of the electronic
degrees of freedom to the mechanical oscillations of the suspended structure.
Here, we investigate theoretically the consequences of a capacitive
electromechanical interaction when the supporting beam is brought close to the
Euler buckling instability by a lateral compressive strain. Our central result
is that the low-bias current blockade, originating from the electromechanical
coupling for the classical resonator, is strongly enhanced near the Euler
instability. We predict that the bias voltage below which transport is blocked
increases by orders of magnitude for typical parameters. This mechanism may
make the otherwise elusive classical current blockade experimentally
observable.Comment: 15 pages, 10 figures, 1 table; published versio
The Puzzle of the Flyby Anomaly
Close planetary flybys are frequently employed as a technique to place
spacecraft on extreme solar system trajectories that would otherwise require
much larger booster vehicles or may not even be feasible when relying solely on
chemical propulsion. The theoretical description of the flybys, referred to as
gravity assists, is well established. However, there seems to be a lack of
understanding of the physical processes occurring during these dynamical
events. Radio-metric tracking data received from a number of spacecraft that
experienced an Earth gravity assist indicate the presence of an unexpected
energy change that happened during the flyby and cannot be explained by the
standard methods of modern astrodynamics. This puzzling behavior of several
spacecraft has become known as the flyby anomaly. We present the summary of the
recent anomalous observations and discuss possible ways to resolve this puzzle.Comment: 6 pages, 1 figure. Accepted for publication by Space Science Review
3+1D hydrodynamic simulation of relativistic heavy-ion collisions
We present MUSIC, an implementation of the Kurganov-Tadmor algorithm for
relativistic 3+1 dimensional fluid dynamics in heavy-ion collision scenarios.
This Riemann-solver-free, second-order, high-resolution scheme is characterized
by a very small numerical viscosity and its ability to treat shocks and
discontinuities very well. We also incorporate a sophisticated algorithm for
the determination of the freeze-out surface using a three dimensional
triangulation of the hyper-surface. Implementing a recent lattice based
equation of state, we compute p_T-spectra and pseudorapidity distributions for
Au+Au collisions at root s = 200 GeV and present results for the anisotropic
flow coefficients v_2 and v_4 as a function of both p_T and pseudorapidity. We
were able to determine v_4 with high numerical precision, finding that it does
not strongly depend on the choice of initial condition or equation of state.Comment: 16 pages, 11 figures, version accepted for publication in PRC,
references added, minor typos corrected, more detailed discussion of
freeze-out routine adde
A constrained random-force model for weakly bending semiflexible polymers
The random-force (Larkin) model of a directed elastic string subject to
quenched random forces in the transverse directions has been a paradigm in the
statistical physics of disordered systems. In this brief note, we investigate a
modified version of the above model where the total transverse force along the
polymer contour and the related total torque, in each realization of disorder,
vanish. We discuss the merits of adding these constraints and show that they
leave the qualitative behavior in the strong stretching regime unchanged, but
they reduce the effects of the random force by significant numerical
prefactors. We also show that a transverse random force effectively makes the
filament softer to compression by inducing undulations. We calculate the
related linear compression coefficient in both the usual and the constrained
random force model.Comment: 4 pages, 1 figure, accepted for publication in PR
A nonlocal connection between certain linear and nonlinear ordinary differential equations/oscillators
We explore a nonlocal connection between certain linear and nonlinear
ordinary differential equations (ODEs), representing physically important
oscillator systems, and identify a class of integrable nonlinear ODEs of any
order. We also devise a method to derive explicit general solutions of the
nonlinear ODEs. Interestingly, many well known integrable models can be
accommodated into our scheme and our procedure thereby provides further
understanding of these models.Comment: 12 pages. J. Phys. A: Math. Gen. 39 (2006) in pres
Synchronization Transition in the Kuramoto Model with Colored Noise
We present a linear stability analysis of the incoherent state in a system of
globally coupled, identical phase oscillators subject to colored noise. In that
we succeed to bridge the extreme time scales between the formerly studied and
analytically solvable cases of white noise and quenched random frequencies.Comment: 4 pages, 2 figure
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