Ma-Xu quantization rule and exact WKB condition for translationally shape invariant potentials

For translationally shape invariant potentials, the exact quantization rule proposed by Ma and Xu is a direct consequence of exactness of the modified WKB quantization condition proved by Barclay. We propose here a very direct alternative way to calculate the appropriate correction for the whole class of translationally shape invariant potentials

From principal component to direct coupling analysis of coevolution in proteins: Low-eigenvalue modes are needed for structure prediction

Various approaches have explored the covariation of residues in multiple-sequence alignments of homologous proteins to extract functional and structural information. Among those are principal component analysis (PCA), which identifies the most correlated groups of residues, and direct coupling analysis (DCA), a global inference method based on the maximum entropy principle, which aims at predicting residue-residue contacts. In this paper, inspired by the statistical physics of disordered systems, we introduce the Hopfield-Potts model to naturally interpolate between these two approaches. The Hopfield-Potts model allows us to identify relevant 'patterns' of residues from the knowledge of the eigenmodes and eigenvalues of the residue-residue correlation matrix. We show how the computation of such statistical patterns makes it possible to accurately predict residue-residue contacts with a much smaller number of parameters than DCA. This dimensional reduction allows us to avoid overfitting and to extract contact information from multiple-sequence alignments of reduced size. In addition, we show that low-eigenvalue correlation modes, discarded by PCA, are important to recover structural information: the corresponding patterns are highly localized, that is, they are concentrated in few sites, which we find to be in close contact in the three-dimensional protein fold.Comment: Supporting information can be downloaded from: http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.100317

Isotopic Scaling of Heavy Projectile Residues from the collisions of 25 MeV/nucleon 86Kr with 124Sn, 112Sn and 64Ni, 58Ni

The scaling of the yields of heavy projectile residues from the reactions of 25 MeV/nucleon 86Kr projectiles with 124Sn,112Sn and 64Ni, 58Nitargets is studied. Isotopically resolved yield distributions of projectile fragments in the range Z=10-36 from these reaction pairs were measured with the MARS recoil separator in the angular range 2.7-5.3 degrees. The velocities of the residues, monotonically decreasing with Z down to Z~26-28, are employed to characterize the excitation energy. The yield ratios R21(N,Z) for each pair of systems are found to exhibit isotopic scaling (isoscaling), namely, an exponential dependence on the fragment atomic number Z and neutron number N. The isoscaling is found to occur in the residue Z range corresponding to the maximum observed excitation energies. The corresponding isoscaling parameters are alpha=0.43 and beta=-0.50 for the Kr+Sn system and alpha=0.27 and beta=-0.34 for the Kr+Ni system. For the Kr+Sn system, for which the experimental angular acceptance range lies inside the grazing angle, isoscaling was found to occur for Z<26 and N<34. For heavier fragments from Kr+Sn, the parameters vary monotonically, alpha decreasing with Z and beta increasing with N. This variation is found to be related to the evolution towards isospin equilibration and, as such, it can serve as a tracer of the N/Z equilibration process. The present heavy-residue data extend the observation of isotopic scaling from the intermediate mass fragment region to the heavy-residue region. Such high-resolution mass spectrometric data can provide important information on the role of isospin in peripheral and mid-peripheral collisions, complementary to that accessible from modern large-acceptance multidetector devices.Comment: 8 pages, 6 figures, submitted to Phys. Rev.

Thermal control system corrosion study

During the development of an expert system for autonomous control of the Space Station Thermal Control System (TCS), the thermal performance of the Brassboard TCS began to gradually degrade. This degradation was due to filter clogging by metallic residue. A study was initiated to determine the source of the residue and the basic cause of the corrosion. The investigation focused on the TCS design, materials compatibility, Ames operating and maintenance procedures, and chemical analysis of the residue and of the anhydrous ammonia used as the principal refrigerant. It was concluded that the corrosion mechanisms involved two processes: the reaction of water alone with large, untreated aluminum parts in a high pH environment and the presence of chlorides and chloride salts. These salts will attack the aluminum oxide layer and may enable galvanic corrosion between the aluminum and the more noble stainless steel and other metallic elements present. Recommendations are made for modifications to the system design, the materials used, and the operating and maintenance procedures, which should largely prevent the recurrence of these corrosion mechanisms

Multi-mode solitons in the classical Dicke-Jaynes-Cummings-Gaudin Model

We present a detailed analysis of the classical Dicke-Jaynes-Cummings-Gaudin integrable model, which describes a system of $n$ spins coupled to a single harmonic oscillator. We focus on the singularities of the vector-valued moment map whose components are the $n+1$ mutually commuting conserved Hamiltonians. The level sets of the moment map corresponding to singular values may be viewed as degenerate and often singular Arnold-Liouville torii. A particularly interesting example of singularity corresponds to unstable equilibrium points where the rank of the moment map is zero, or singular lines where the rank is one. The corresponding level sets can be described as a reunion of smooth strata of various dimensions. Using the Lax representation, the associated spectral curve and the separated variables, we show how to construct explicitely these level sets. A main difficulty in this task is to select, among possible complex solutions, the physically admissible family for which all the spin components are real. We obtain explicit solutions to this problem in the rank zero and one cases. Remarkably this corresponds exactly to solutions obtained previously by Yuzbashyan and whose geometrical meaning is therefore revealed. These solutions can be described as multi-mode solitons which can live on strata of arbitrary large dimension. In these solitons, the energy initially stored in some excited spins (or atoms) is transferred at finite times to the oscillator mode (photon) and eventually comes back into the spin subsystem. But their multi-mode character is reflected by a large diversity in their shape, which is controlled by the choice of the initial condition on the stratum

Improved Quantum Hard-Sphere Ground-State Equations of State

The London ground-state energy formula as a function of number density for a system of identical boson hard spheres, corrected for the reduced mass of a pair of particles in a sphere-of-influence picture, and generalized to fermion hard-sphere systems with two and four intrinsic degrees of freedom, has a double-pole at the ultimate \textit{regular} (or periodic, e.g., face-centered-cubic) close-packing density usually associated with a crystalline branch. Improved fluid branches are contructed based upon exact, field-theoretic perturbation-theory low-density expansions for many-boson and many-fermion systems, appropriately extrapolated to intermediate densities, but whose ultimate density is irregular or \textit{random} closest close-packing as suggested in studies of a classical system of hard spheres. Results show substantially improved agreement with the best available Green-function Monte Carlo and diffusion Monte Carlo simulations for bosons, as well as with ladder, variational Fermi hypernetted chain, and so-called L-expansion data for two-component fermions.Comment: 15 pages and 7 figure

Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach

The heavy quark pole mass in perturbation theory suffers from a renormalon caused, inherent uncertainty of $O(\Lambda_{\rm QCD})$. This fundamental difficulty of determining the pole mass to an accuracy better than the inherent uncertainty can be overcome by direct resummation of the first infrared renormalon. We show how a properly defined pole mass as well as the $\bar {\rm MS}$ mass for the top and bottom quarks can be determined accurately from the $O(m\alpha_s^5)$ quarkonium ground state energy.Comment: 16 pages; published versio