Fluctuating Fronts as Correlated Extreme Value Problems: An Example of Gaussian Statistics

In this paper, we view fluctuating fronts made of particles on a one-dimensional lattice as an extreme value problem. The idea is to denote the configuration for a single front realization at time $t$ by the set of co-ordinates $\{k_i(t)\}\equiv[k_1(t),k_2(t),...,k_{N(t)}(t)]$ of the constituent particles, where $N(t)$ is the total number of particles in that realization at time $t$. When $\{k_i(t)\}$ are arranged in the ascending order of magnitudes, the instantaneous front position can be denoted by the location of the rightmost particle, i.e., by the extremal value $k_f(t)=\text{max}[k_1(t),k_2(t),...,k_{N(t)}(t)]$. Due to interparticle interactions, $\{k_i(t)\}$ at two different times for a single front realization are naturally not independent of each other, and thus the probability distribution $P_{k_f}(t)$ [based on an ensemble of such front realizations] describes extreme value statistics for a set of correlated random variables. In view of the fact that exact results for correlated extreme value statistics are rather rare, here we show that for a fermionic front model in a reaction-diffusion system, $P_{k_f}(t)$ is Gaussian. In a bosonic front model however, we observe small deviations from the Gaussian.Comment: 6 pages, 3 figures, miniscule changes on the previous version, to appear in Phys. Rev.

Qualitative behavior of three species food chain around inner equilibrium point: spectral analysis

This work deals with analytical investigation of local qualitative temporal behavior around inner equilibrium point of a model for three species food chain, studied earlier by Hastings and Powel and others. As an initial step towards the spectral analysis of the model, the governing equations have been split into linear and nonlinear parts around arbitrary equilibrium point. The explicit parameter dependence of eigenvalues of Jacobi matrix associated to the linear part have been derived. Analyzing these expressions in conjunction with some pedagogical analysis, a lot of predictions on stable, unstable or chaotic change of species have been highlighted. Agreement of predictions of this work with available numerical or semi-analytical studies suggest the utility of analytical results derived here for further investigation/analysis of the model as desired by earlier works

Monomer dynamics of a wormlike chain

We derive the stochastic equations of motion for a tracer that is tightly attached to a semiflexible polymer and confined or agitated by an externally controlled potential. The generalised Langevin equation, the power spectrum, and the mean-square displacement for the tracer dynamics are explicitly constructed from the microscopic equations of motion for a weakly bending wormlike chain by a systematic coarse-graining procedure. Our accurate analytical expressions should provide a convenient starting point for further theoretical developments and for the analysis of various single-molecule experiments and of protein shape fluctuations.Comment: 6 pages, 4 figure

Near-infrared photoabsorption by C(60) dianions in a storage ring

We present a detailed study of the electronic structure and the stability of C(60) dianions in the gas phase. Monoanions were extracted from a plasma source and converted to dianions by electron transfer in a Na vapor cell. The dianions were then stored in an electrostatic ring, and their near-infrared absorption spectrum was measured by observation of laser induced electron detachment. From the time dependence of the detachment after photon absorption, we conclude that the reaction has contributions from both direct electron tunneling to the continuum and vibrationally assisted tunneling after internal conversion. This implies that the height of the Coulomb barrier confining the attached electrons is at least similar to 1.5 eV. For C(60)(2-) ions in solution electron spin resonance measurements have indicated a singlet ground state, and from the similarity of the absorption spectra we conclude that also the ground state of isolated C(60)(2-) ions is singlet. The observed spectrum corresponds to an electronic transition from a t(1u) lowest unoccupied molecular orbital (LUMO) of C(60) to the t(1g) LUMO+1 level. The electronic levels of the dianion are split due to Jahn-Teller coupling to quadrupole deformations of the molecule, and a main absorption band at 10723 cm(-1) corresponds to a transition between the Jahn-Teller ground states. Also transitions from pseudorotational states with 200 cm(-1) and (probably) 420 cm(-1) excitation are observed. We argue that a very broad absorption band from about 11 500 cm(-1) to 13 500 cm(-1) consists of transitions to so-called cone states, which are Jahn-Teller states on a higher potential-energy surface, stabilized by a pseudorotational angular momentum barrier. A previously observed, high-lying absorption band for C(60)(-) may also be a transition to a cone state

CAUSES OF DISPOSAL OF MURRAH BUFFALO FROM AN ORGANISED HERD

The present study comprised of 602 disposal records of adult Murrah buffaloes , spread over a period of 16 years from 1985 to 2000 at NDRI, Karnal, Haryana. Analysed data showed that the reproductive problems (38.62), low milk production (24.01) and udder problems (22.76) were the three major reasons of culling in adult Murrah buffaloes . The culling of cows due to involuntary reason (reproductive problems, udder problems and locomotive disorders) accounted for nearly 63.68 percent of total culling in Murrah buffaloes in the NDRI herd. The data revealed that maximum mortality occurred due to digestive problems accounting for 30.89 percent followed by cardio-vascular problems (26.02 percent), respiratory problems (21.14 percent), parasitic problems (8.13 percent) and uro-genital problems (5.69 percent). The results showed that there is a scope for further improvement in production and reproductive efficiency through better monitoring of reproduction and udder health status of the buffaloes. The high involuntary culling rate not only makes the dairy enterprises economically less profitable but also reduces the genetic improvement by lowering the selection differential for milk production

Logarithmic perturbation theory for radial Klein-Gordon equation with screened Coulomb potentials via ℏ\hbar expansions

The explicit semiclassical treatment of logarithmic perturbation theory for the bound-state problem within the framework of the radial Klein-Gordon equation with attractive real-analytic screened Coulomb potentials, contained time-component of a Lorentz four-vector and a Lorentz-scalar term, is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both for ground and excited states have been obtained. As an example, the perturbation expansions for the energy eigenvalues for the Hulth\'en potential containing the vector part as well as the scalar component are considered.Comment: 14 pages, to be submitted to Journal of Physics

Approximate Solution of the effective mass Klein-Gordon Equation for the Hulthen Potential with any Angular Momentum

The radial part of the effective mass Klein-Gordon equation for the Hulthen potential is solved by making an approximation to the centrifugal potential. The Nikiforov-Uvarov method is used in the calculations. Energy spectra and the corresponding eigenfunctions are computed. Results are also given for the case of constant mass.Comment: 12 page

Anomalous zipping dynamics and forced polymer translocation

We investigate by Monte Carlo simulations the zipping and unzipping dynamics of two polymers connected by one end and subject to an attractive interaction between complementary monomers. In zipping, the polymers are quenched from a high temperature equilibrium configuration to a low temperature state, so that the two strands zip up by closing up a "Y"-fork. In unzipping, the polymers are brought from a low temperature double stranded configuration to high temperatures, so that the two strands separate. Simulations show that the unzipping time, $\tau_u$, scales as a function of the polymer length as $\tau_u \sim L$, while the zipping is characterized by anomalous dynamics $\tau_z \sim L^\alpha$ with $\alpha = 1.37(2)$. This exponent is in good agreement with simulation results and theoretical predictions for the scaling of the translocation time of a forced polymer passing through a narrow pore. We find that the exponent $\alpha$ is robust against variations of parameters and temperature, whereas the scaling of $\tau_z$ as a function of the driving force shows the existence of two different regimes: the weak forcing ($\tau_z \sim 1/F$) and strong forcing ($\tau_z$ independent of $F$) regimes. The crossover region is possibly characterized by a non-trivial scaling in $F$, matching the prediction of recent theories of polymer translocation. Although the geometrical setup is different, zipping and translocation share thus the same type of anomalous dynamics. Systems where this dynamics could be experimentally investigated are DNA (or RNA) hairpins: our results imply an anomalous dynamics for the hairpins closing times, but not for the opening times.Comment: 15 pages, 9 figure