9,018 research outputs found
Exact Charged 2-Body Motion and the Static Balance Condition in Lineal Gravity
We find an exact solution to the charged 2-body problem in
dimensional lineal gravity which provides the first example of a relativistic
system that generalizes the Majumdar-Papapetrou condition for static balance.Comment: latex,7 pages, 2 figure
Individual and collective dynamics of self-propelled soft particles
Deformable self-propelled particles provide us with one of the most important
nonlinear dissipative systems, which are related, for example, to the motion of
microorganisms. It is emphasized that this is a subject of localized objects in
non-equilibrium open systems. We introduce a coupled set of ordinary
differential equations to study various dynamics of individual soft particles
due to the nonlinear couplings between migration, spinning and deformation. By
introducing interactions among the particles, the collective dynamics and its
collapse are also investigated by changing the particle density and the
interaction strength. We stress that assemblies of self-propelled particles
also exhibit a variety of non-equilibrium localized patterns
Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor
An asymptotic equation of motion for the pattern interface in the
domain-forming reaction-diffusion systems is derived. The free boundary problem
is reduced to the universal equation of non-local contour dynamics in two
dimensions in the parameter region where a pattern is not far from the points
of the transverse instabilities of its walls. The contour dynamics is studied
numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It
is shown that in the asymptotic limit the transverse instability of the
localized domains leads to their splitting and formation of the multidomain
pattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys.
Rev.
Exact Relativistic Two-Body Motion in Lineal Gravity
We consider the N-body problem in (1+1) dimensional lineal gravity. For 2
point masses (N=2) we obtain an exact solution for the relativistic motion. In
the equal mass case we obtain an explicit expression for their proper
separation as a function of their mutual proper time. Our solution gives the
exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: latex, 11 pages, 2 figures, final version to appear in Phys. Rev.
Let
Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity
We present the exact solution of two-body motion in (1+1) dimensional dilaton
gravity by solving the constraint equations in the canonical formalism. The
determining equation of the Hamiltonian is derived in a transcendental form and
the Hamiltonian is expressed for the system of two identical particles in terms
of the Lambert function. The function has two real branches which join
smoothly onto each other and the Hamiltonian on the principal branch reduces to
the Newtonian limit for small coupling constant. On the other branch the
Hamiltonian yields a new set of motions which can not be understood as
relativistically correcting the Newtonian motion. The explicit trajectory in
the phase space is illustrated for various values of the energy. The
analysis is extended to the case of unequal masses. The full expression of
metric tensor is given and the consistency between the solution of the metric
and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure
A simple stochastic model for the evolution of protein lengths
We analyse a simple discrete-time stochastic process for the theoretical
modeling of the evolution of protein lengths. At every step of the process a
new protein is produced as a modification of one of the proteins already
existing and its length is assumed to be random variable which depends only on
the length of the originating protein. Thus a Random Recursive Trees (RRT) is
produced over the natural integers. If (quasi) scale invariance is assumed, the
length distribution in a single history tends to a lognormal form with a
specific signature of the deviations from exact gaussianity. Comparison with
the very large SIMAP protein database shows good agreement.Comment: 12 pages, 4 figure
From Labyrinthine Patterns to Spiral Turbulence
A new mechanism for spiral vortex nucleation in nongradient reaction
diffusion systems is proposed. It involves two key ingredients: An Ising-Bloch
type front bifurcation and an instability of a planar front to transverse
perturbations. Vortex nucleation by this mechanism plays an important role in
inducing a transition from labyrinthine patterns to spiral turbulence. PACS
numbers: 05.45.+b, 82.20.MjComment: 4 pages uuencoded compressed postscrip
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