Thermodynamic Length, Time, Speed and Optimum Path to Minimize Entropy Production

In addition to the Riemannian metricization of the thermodynamic state space, local relaxation times offer a natural time scale, too. Generalizing existing proposals, we relate {\it thermodynamic} time scale to the standard kinetic coefficients of irreversible thermodynamics. Criteria for minimum entropy production in slow, slightly irreversible processes are discussed. Euler-Lagrange equations are derived for optimum thermodynamic control for fixed clock-time period as well as for fixed {\it thermodynamic} time period. Only this latter requires constant thermodynamic speed as the optimum control proposed earlier. An easy-to-implement stepwise algorithm is constructed to realize control at constant thermodynamic speed. Since thermodynamic time is shown to correspond to the number of steps, thus the sophisticated task of determining thermodynamic time in real control problems can be substituted by measuring ordinary intensive variables. Most remarkably, optimum paths are Riemannian geodesics which would not be the case had we used ordinary time.Comment: revised version with essential corrections, LaTeX 13p

Heavy quarks or compactified extra dimensions in the core of hybrid stars

Neutron stars with extremely high central energy density are natural laboratories to investigate the appearance and the properties of compactified extra dimensions with small compactification radius, if they exist. Using the same formalism, these exotic hybrid stars can be described as neutron stars with quark core, where the high energy density allows the presence of heavy quarks (c, b, t). We compare the two scenarios for hybrid stars and display their characteristic features.Comment: Talk given at 4th International Workshop on New Worlds in Astroparticle Physics, Faro, Portugal, 5-7, Sep 2002. 10 pages, 6 EPS figure

Dates, Caries, and Early Tooth Loss During the Iron Age of Oman

Eine Ernährung aus fermentierbaren Kohlenhydraten ist bekannterweise hoch kariogen, besonders im Falle von zuckerhaltigem Essen wie zum Beispiel Datteln. Diese Ernährung ist bei der späteisenzeitlichen Samad-zeitlichen Bevölkerung Omans zu beobachten. 32 Erwachsene und 5 Jugendliche dienten für diese Studie als Erhebung. Vorzeitiger Zahnverlust war in allen Fällen nachweisbar

Family of solvable generalized random-matrix ensembles with unitary symmetry

We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread function'. Various choices of the spread function lead to a variety of possible generalized RMEs, which show deviations from the well-known Gaussian RME originally proposed by Wigner. We obtain the correlation functions of such generalized ensembles exactly, and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality.Comment: 4 pages, to be published in Phys. Rev. E, Rapid Com

Some Physical Consequences of Abrupt Changes in the Multipole Moments of a Gravitating Body

The Barrab\`es-Israel theory of light-like shells in General Relativity is used to show explicitly that in general a light-like shell is accompanied by an impulsive gravitational wave. The gravitational wave is identified by its Petrov Type N contribution to a Dirac delta-function term in the Weyl conformal curvature tensor (with the delta-function singular on the null hypersurface history of the wave and shell). An example is described in which an asymptotically flat static vacuum Weyl space-time experiences a sudden change across a null hypersurface in the multipole moments of its isolated axially symmetric source. A light-like shell and an impulsive gravitational wave are identified, both having the null hypersurface as history. The stress-energy in the shell is dominated (at large distance from the source) by the jump in the monopole moment (the mass) of the source with the jump in the quadrupole moment mainly responsible for the stress being anisotropic. The gravitational wave owes its existence principally to the jump in the quadrupole moment of the source confirming what would be expected.Comment: 26 pages, tex, no figures, to appear in Phys.Rev.

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure

Integrated random processes exhibiting long tails, finite moments and 1/f spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution -which can be obtained from our model in certain limits- which has no finite moments. The evaluation of the power spectrum and the form of the probability density function in the tails of the distribution shows that the model exhibits a 1/f spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Levy processes together with another part representing the deviation of our model from the Levy process. This allows our process to be viewed as a generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.

BLUF Domain Function Does Not Require a Metastable Radical Intermediate State

BLUF (blue light using flavin) domain proteins are an important family of blue light-sensing proteins which control a wide variety of functions in cells. The primary light-activated step in the BLUF domain is not yet established. A number of experimental and theoretical studies points to a role for photoinduced electron transfer (PET) between a highly conserved tyrosine and the flavin chromophore to form a radical intermediate state. Here we investigate the role of PET in three different BLUF proteins, using ultrafast broadband transient infrared spectroscopy. We characterize and identify infrared active marker modes for excited and ground state species and use them to record photochemical dynamics in the proteins. We also generate mutants which unambiguously show PET and, through isotope labeling of the protein and the chromophore, are able to assign modes characteristic of both flavin and protein radical states. We find that these radical intermediates are not observed in two of the three BLUF domains studied, casting doubt on the importance of the formation of a population of radical intermediates in the BLUF photocycle. Further, unnatural amino acid mutagenesis is used to replace the conserved tyrosine with fluorotyrosines, thus modifying the driving force for the proposed electron transfer reaction; the rate changes observed are also not consistent with a PET mechanism. Thus, while intermediates of PET reactions can be observed in BLUF proteins they are not correlated with photoactivity, suggesting that radical intermediates are not central to their operation. Alternative nonradical pathways including a keto–enol tautomerization induced by electronic excitation of the flavin ring are considered

The Limiting Distribution of the Trace of a Random Plane Partition

We study the asymptotic behaviour of the trace (the sum of the diagonal parts) of a plane partition of the positive integer n, assuming that this parfition is chosen uniformly at random from the set of all such partitions.Comment: 19 page