Coupling hydrophobic, dispersion, and electrostatic contributions in continuum solvent models

Recent studies of the hydration of micro- and nanoscale solutes have demonstrated a strong {\it coupling} between hydrophobic, dispersion and electrostatic contributions, a fact not accounted for in current implicit solvent models. We present a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy with respect to a solvent volume exclusion function. The solvent accessible surface is output of our theory. Our method is illustrated with the hydration of alkane-assembled solutes on different length scales, and captures the strong sensitivity to the particular form of the solute-solvent interactions in agreement with recent computer simulations.Comment: 11 pages, 2 figure

An isoperimetric problem for point interactions

We consider Hamiltonian with $N$ point interactions in $\R^d, d=2,3,$ all with the same coupling constant, placed at vertices of an equilateral polygon \PP_N. It is shown that the ground state energy is locally maximized by a regular polygon. The question whether the maximum is global is reduced to an interesting geometric problem.Comment: LaTeX 2e, 10 page

Resting and reactive frontal brain electrical activity (EEG) among a non-clinical sample of socially anxious adults: does concurrent depressive mood matter?

A number of studies have noted that the pattern of resting frontal brain electrical activity (EEG) is related to individual differences in affective style in healthy infants, children, and adults and some clinical populations when symptoms are reduced or in remission. We measured self-reported trait shyness and sociability, concurrent depressive mood, and frontal brain electrical activity (EEG) at rest and in anticipation of a speech task in a non-clinical sample of healthy young adults selected for high and low social anxiety. Although the patterns of resting and reactive frontal EEG asymmetry did not distinguish among individual differences in social anxiety, the pattern of resting frontal EEG asymmetry was related to trait shyness after controlling for concurrent depressive mood. Individuals who reported a higher degree of shyness were likely to exhibit greater relative right frontal EEG activity at rest. However, trait shyness was not related to frontal EEG asymmetry measured during the speech-preparation task, even after controlling for concurrent depressive mood. These findings replicate and extend prior work on resting frontal EEG asymmetry and individual differences in affective style in adults. Findings also highlight the importance of considering concurrent emotional states of participants when examining psychophysiological correlates of personality

An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given $\tau>0$, the free plate eigenvalues $\omega$ and eigenfunctions $u$ are determined by the equation $\Delta\Delta u-\tau\Delta u = \omega u$ together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term $|D^2u|^2$. We adapt Weinberger's method from the corresponding free membrane problem, taking the fundamental modes of the unit ball as trial functions. These solutions are a linear combination of Bessel and modified Bessel functions.Comment: PhD thesis. Papers are in preparatio

Brachial Artery Vasculitis and Associated Stenosis Presenting as Elbow Pain in a 16-Year-Old Soccer Player: A Case Report

Chronic vascular occlusion in the upper extremity can result from repetitive trauma, atherosclerosis, proximal embolic events, hypercoagulable states, and systemic diseases such as collagen vascular disease and vasculitis. Considerable functional impairment can result from these maladies; however, sometimes the condition develops slowly with minimal effect on the patient. We describe a 16-year-old soccer player with slow-progressing elbow pain and loss of range in motion caused by brachial artery vasculitis and resultant brachial arterial stenosis. Although vascular insults and lesions rarely cause chronic vascular occlusion, physicians should consider this possibility in patients with localized pain or atrophy, especially if the condition develops slowly

Segue Between Favorable and Unfavorable Solvation

Solvation of small and large clusters are studied by simulation, considering a range of solvent-solute attractive energy strengths. Over a wide range of conditions, both for solvation in the Lennard-Jones liquid and in the SPC model of water, it is shown that the mean solvent density varies linearly with changes in solvent-solute adhesion or attractive energy strength. This behavior is understood from the perspective of Weeks' theory of solvation [Ann. Rev. Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.Comment: 8 pages, 7 figure

Resting and reactive frontal brain electrical activity (EEG) among a non-clinical sample of socially anxious adults: Does concurrent depressive mood matter?

A number of studies have noted that the pattern of resting frontal brain electrical activity (EEG) is related to individual differences in affective style in healthy infants, children, and adults and some clinical populations when symptoms are reduced or in remission. We measured self-reported trait shyness and sociability, concurrent depressive mood, and frontal brain electrical activity (EEG) at rest and in anticipation of a speech task in a non-clinical sample of healthy young adults selected for high and low social anxiety. Although the patterns of resting and reactive frontal EEG asymmetry did not distinguish among individual differences in social anxiety, the pattern of resting frontal EEG asymmetry was related to trait shyness after controlling for concurrent depressive mood. Individuals who reported a higher degree of shyness were likely to exhibit greater relative right frontal EEG activity at rest. However, trait shyness was not related to frontal EEG asymmetry measured during the speech-preparation task, even after controlling for concurrent depressive mood. These findings replicate and extend prior work on resting frontal EEG asymmetry and individual differences in affective style in adults. Findings also highlight the importance of considering concurrent emotional states of participants when examining psychophysiological correlates of personality

Approximation of the critical buckling factor for composite panels

This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure