Water and Alanine: From Puddles(32) to Ponds(49)

The solvation of alanine is investigated, with a focus on adding a sufficient number of discrete water molecules to determine the first solvation shell for both the nonionized (N) and zwitterionic (Z) forms to converge the enthalpy of solvation and the enthalpy difference for the two forms of alanine. Monte Carlo sampling was employed using the generalized effective fragment potential (EFP) method to determine the global minimum of both conformers, with the number of EFP water molecules ranging from 32−49. A subset of sampled geometries were optimized with second-order perturbation theory (MP2) using the 6-31++G(d,p) basis set. Single point energies were calculated at these geometries using the polarizable continuum model (PCM). The predicted 298.15 K enthalpy of solvation ranges for MP2/6-31++G(d,p) and MP2+PCM//MP2/6-31++G(d,p) are 10.0−13.2 kcal/mol and 10.1−12.6 kcal/mol, respectively

Absence of Fragmentation in Two-Dimensional Bose-Einstein Condensation

We investigate the possibility that the BEC-like phenomena recently detected on two-dimensional finite trapped systems consist of fragmented condensates. We derive and diagonalize the one-body density matrix of a two-dimensional isotropically trapped Bose gas at finite temperature. For the ideal gas, the procedure reproduces the exact harmonic-oscillator eigenfunctions and the Bose distribution. We use a new collocation-minimization method to study the interacting gas in the Hartree-Fock approximation and obtain a ground-state wavefunction and condensate fraction consistent with those obtained by other methods. The populations of the next few eigenstates increase at the expense of the ground state but continue to be negligible; this supports the conclusion that two-dimensional BEC is into a single state.Comment: 6 pages, 1 figur

Exclusion Statistics in a two-dimensional trapped Bose gas

We briefly explain the notion of exclusion statistics and in particular discuss the concept of an ideal exclusion statistics gas. We then review a recent work where it is demonstrated that a {\em two-dimensional} Bose gas with repulsive delta function interactions obeys ideal exclusion statistics, with a fractional parameter related to the interaction strength.Comment: 10 pages, RevTeX. Proceedings of the Salerno workshop "Theory of Quantum Gases and Quantum Coherence", to appear in a special issue of J.Phys. B, Dec. 200

Embedding the affine complement of three intersecting lines in a finite projective plane

An (r, 1)–design is a pair (V, F) where V is a ν–set and F is a family of non-null subsets of V (b in number) which satisfy the following. (1) Every pair of distinct members of V is contained in precisely one member of F. (2) Every member of V occurs in precisely r members of F. A pseudo parallel complement PPC(n, α) is an (n+1, 1)–design with ν=n2−αn and b≦n2+n−α in which there are at least n−α a blocks of size n. A pseudo intersecting complement PIC(n, α) is an (n+1, 1)–design with ν=n2−αn+α−1 and b≦n2+n−α in which there are at least n−α+1 blocks of size n−1. It has previously been shown that for α≦4, every PIC(n, α) can be embedded in a PPC(n, α−1) and that for n>(α4−2α3+2α2+α−2)/2, every PPC(n, α) can be embedded in a finite projective plane of order n. In this paper we investigate the case of α=3 and show that any PIC(n, 3) is embeddable in a PPC(n,2) provided n≧14

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Anisotropic Spin Diffusion in Trapped Boltzmann Gases

Recent experiments in a mixture of two hyperfine states of trapped Bose gases show behavior analogous to a spin-1/2 system, including transverse spin waves and other familiar Leggett-Rice-type effects. We have derived the kinetic equations applicable to these systems, including the spin dependence of interparticle interactions in the collision integral, and have solved for spin-wave frequencies and longitudinal and transverse diffusion constants in the Boltzmann limit. We find that, while the transverse and longitudinal collision times for trapped Fermi gases are identical, the Bose gas shows diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions leads to the non-conservation of transverse spin, which in turn has novel effects on the hydrodynamic modes.Comment: 10 pages, 4 figures; submitted to PR

Fluid Restriction Dehydration Increase Core Temperature During Endurance Exercise Compared to Exercise Induced Dehydration

International Journal of Exercise Science 15(2): 166-176, 2022. This study aimed to evaluate the difference in heart rate and core temperature during aerobic exercise between two forms of dehydration: exercise-induced (EI) and fluid restricted (FR). Twenty-two subjects (N = 22; 83.35 ± 13.92 kg) completed the current study, performing a familiarization session, a pre-experimental exercise session, and two exercise testing sessions. The EI exercise trial (81.52 ± 13.72 kg) was conducted after performing exercise in a hot environment to lose three to four percent of body weight and partial rehydration. The FR exercise trial (81.53 ± 14.14 kg) was completed after 12 hours of fluid restriction. During both exercise sessions, subjects pedaled against a set resistance of 130 watts for 30 minutes. The main effect of hydration on Tc was significant, F(1, 18) = 4.474, p = .049, ηp2 = .199 (Figure 2) with core temperature being greater during the FR trial compared to the EI trial (FR = 37.58 ± .06°C vs. EI = 37.31 ± .11°C). No significant interaction was found between hydration and time for HR, F(2, 42) = 0.120, p = .887, ηp2 = .006. The main effect of time on HR was significant, F(2, 42) = 119.664, p \u3c .001, ηp2 = .851. Fluid restriction was associated with an increase in core temperature. An increased core temperature may negatively influence performance, and care should be taken to ensure proper hydration