851 research outputs found
Birth and death processes and quantum spin chains
This papers underscores the intimate connection between the quantum walks
generated by certain spin chain Hamiltonians and classical birth and death
processes. It is observed that transition amplitudes between single excitation
states of the spin chains have an expression in terms of orthogonal polynomials
which is analogous to the Karlin-McGregor representation formula of the
transition probability functions for classes of birth and death processes. As
an application, we present a characterization of spin systems for which the
probability to return to the point of origin at some time is 1 or almost 1.Comment: 14 page
Aging to non-Newtonian hydrodynamics in a granular gas
The evolution to the steady state of a granular gas subject to simple shear
flow is analyzed by means of computer simulations. It is found that, regardless
of its initial preparation, the system reaches (after a transient period
lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic
regime, even at strong dissipation and for states where the time scale
associated with inelastic cooling is shorter than the one associated with the
irreversible fluxes. Comparison with a simplified rheological model shows a
good agreement.Comment: 6 pages, 4 figures; v2: improved version to be published in EP
An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci
A model of mutation rate evolution for multiple loci under arbitrary
selection is analyzed. Results are obtained using techniques from Karlin (1982)
that overcome the weak selection constraints needed for tractability in prior
studies of multilocus event models. A multivariate form of the reduction
principle is found: reduction results at individual loci combine topologically
to produce a surface of mutation rate alterations that are neutral for a new
modifier allele. New mutation rates survive if and only if they fall below this
surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994)
for a multilocus recombination modifier. Increases in mutation rates at some
loci may evolve if compensated for by decreases at other loci. The strength of
selection on the modifier scales in proportion to the number of germline cell
divisions, and increases with the number of loci affected. Loci that do not
make a difference to marginal fitnesses at equilibrium are not subject to the
reduction principle, and under fine tuning of mutation rates would be expected
to have higher mutation rates than loci in mutation-selection balance. Other
results include the nonexistence of 'viability analogous, Hardy-Weinberg'
modifier polymorphisms under multiplicative mutation, and the sufficiency of
average transmission rates to encapsulate the effect of modifier polymorphisms
on the transmission of loci under selection. A conjecture is offered regarding
situations, like recombination in the presence of mutation, that exhibit
departures from the reduction principle. Constraints for tractability are:
tight linkage of all loci, initial fixation at the modifier locus, and mutation
distributions comprising transition probabilities of reversible Markov chains.Comment: v3: Final corrections. v2: Revised title, reworked and expanded
introductory and discussion sections, added corollaries, new results on
modifier polymorphisms, minor corrections. 49 pages, 64 reference
Notes about the Caratheodory number
In this paper we give sufficient conditions for a compactum in
to have Carath\'{e}odory number less than , generalizing an old result of
Fenchel. Then we prove the corresponding versions of the colorful
Carath\'{e}odory theorem and give a Tverberg type theorem for families of
convex compacta
First-passage and first-exit times of a Bessel-like stochastic process
We study a stochastic process related to the Bessel and the Rayleigh
processes, with various applications in physics, chemistry, biology, economics,
finance and other fields. The stochastic differential equation is , where is the Wiener process. Due to the
singularity of the drift term for , different natures of boundary at
the origin arise depending on the real parameter : entrance, exit, and
regular. For each of them we calculate analytically and numerically the
probability density functions of first-passage times or first-exit times.
Nontrivial behaviour is observed in the case of a regular boundary.Comment: 15 pages, 6 figures, submitted to Physical Review
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Mathematical Structure of Relativistic Coulomb Integrals
We show that the diagonal matrix elements where
are the standard Dirac matrix operators
and the angular brackets denote the quantum-mechanical average for the
relativistic Coulomb problem, may be considered as difference analogs of the
radial wave functions. Such structure provides an independent way of obtaining
closed forms of these matrix elements by elementary methods of the theory of
difference equations without explicit evaluation of the integrals. Three-term
recurrence relations for each of these expectation values are derived as a
by-product. Transformation formulas for the corresponding generalized
hypergeometric series are discussed.Comment: 13 pages, no figure
Stochastic Pulse Switching in a Degenerate Resonant Optical Medium
Using the idealized integrable Maxwell-Bloch model, we describe random
optical-pulse polarization switching along an active optical medium in the
Lambda-configuration with disordered occupation numbers of its lower energy
sub-level pair. The description combines complete integrability and stochastic
dynamics. For the single-soliton pulse, we derive the statistics of the
electric-field polarization ellipse at a given point along the medium in closed
form. If the average initial population difference of the two lower sub-levels
vanishes, we show that the pulse polarization will switch intermittently
between the two circular polarizations as it travels along the medium. If this
difference does not vanish, the pulse will eventually forever remain in the
circular polarization determined by which sub-level is more occupied on
average. We also derive the exact expressions for the statistics of the
polarization-switching dynamics, such as the probability distribution of the
distance between two consecutive switches and the percentage of the distance
along the medium the pulse spends in the elliptical polarization of a given
orientation in the case of vanishing average initial population difference. We
find that the latter distribution is given in terms of the well-known arcsine
law
Position and Role of the BK Channel α Subunit S0 Helix Inferred from Disulfide Crosslinking
The position and role of the unique N-terminal transmembrane (TM) helix, S0, in large-conductance, voltage- and calcium-activated potassium (BK) channels are undetermined. From the extents of intra-subunit, endogenous disulfide bond formation between cysteines substituted for the residues just outside the membrane domain, we infer that the extracellular flank of S0 is surrounded on three sides by the extracellular flanks of TM helices S1 and S2 and the four-residue extracellular loop between S3 and S4. Eight different double cysteine–substituted alphas, each with one cysteine in the S0 flank and one in the S3–S4 loop, were at least 90% disulfide cross-linked. Two of these alphas formed channels in which 90% cross-linking had no effect on the V50 or on the activation and deactivation rate constants. This implies that the extracellular ends of S0, S3, and S4 are close in the resting state and move in concert during voltage sensor activation. The association of S0 with the gating charge bearing S3 and S4 could contribute to the considerably larger electrostatic energy required to activate the BK channel compared with typical voltage-gated potassium channels with six TM helices
Maximum principle and mutation thresholds for four-letter sequence evolution
A four-state mutation-selection model for the evolution of populations of
DNA-sequences is investigated with particular interest in the phenomenon of
error thresholds. The mutation model considered is the Kimura 3ST mutation
scheme, fitness functions, which determine the selection process, come from the
permutation-invariant class. Error thresholds can be found for various fitness
functions, the phase diagrams are more interesting than for equivalent
two-state models. Results for (small) finite sequence lengths are compared with
those for infinite sequence length, obtained via a maximum principle that is
equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure
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