A second eigenvalue bound for the Dirichlet Schroedinger operator

Let $\lambda_i(\Omega,V)$ be the $i$th eigenvalue of the Schr\"odinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \R^n$ and with the positive potential $V$. Following the spirit of the Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential $V_\star$, we prove that $\lambda_2(\Omega,V) \le \lambda_2(S_1,V_\star)$. Here $S_1$ denotes the ball, centered at the origin, that satisfies the condition $\lambda_1(\Omega,V) = \lambda_1(S_1,V_\star)$. Further we prove under the same convexity assumptions on a spherically symmetric potential $V$, that $\lambda_2(B_R, V) / \lambda_1(B_R, V)$ decreases when the radius $R$ of the ball $B_R$ increases. We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density

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

Hydration dynamics at fluorinated protein surfaces

Water-protein interactions dictate many processes crucial to protein function including folding, dynamics, interactions with other biomolecules, and enzymatic catalysis. Here we examine the effect of surface fluorination on water-protein interactions. Modification of designed coiled-coil proteins by incorporation of 5,5,5-trifluoroleucine or (4S)-2-amino-4-methylhexanoic acid enables systematic examination of the effects of side-chain volume and fluorination on solvation dynamics. Using ultrafast fluorescence spectroscopy, we find that fluorinated side chains exert electrostatic drag on neighboring water molecules, slowing water motion at the protein surface

Self Consistent Molecular Field Theory for Packing in Classical Liquids

Building on a quasi-chemical formulation of solution theory, this paper proposes a self consistent molecular field theory for packing problems in classical liquids, and tests the theoretical predictions for the excess chemical potential of the hard sphere fluid. Results are given for the self consistent molecular fields obtained, and for the probabilities of occupancy of a molecular observation volume. For this system, the excess chemical potential predicted is as accurate as the most accurate prior theories, particularly the scaled particle (Percus-Yevick compressibility) theory. It is argued that the present approach is particularly simple, and should provide a basis for a molecular-scale description of more complex solutions.Comment: 6 pages and 5 figure

Geometric Phase, Curvature, and Extrapotentials in Constrained Quantum Systems

We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the external curvature of the constraint manifold, the (Riemannian) curvature of the ambient space, and the constraining potential. In particular, we find the remarkable fact that the twisting of the constraining potential appears as a gauge potential in the constrained Hamiltonian. This gauge potential is an example of geometric phase, closely related to that originally discussed by Berry. The constrained Hamiltonian also contains an effective potential depending on the external curvature of the constraint manifold, the curvature of the ambient space, and the twisting of the constraining potential. The general nature of our analysis allows applications to a wide variety of problems, such as rigid molecules, the evolution of molecular systems along reaction paths, and quantum strip waveguides.Comment: 27 pages with 1 figure, submitted to Phys. Rev.

Risk Factors for Moral Injury Among Canadian Armed Forces Personnel

Objectives: The traumatic nature of high-risk military deployment events, such as combat, is well-recognized. However, whether other service-related events and demographic factors increase the risk of moral injury (MI), which is defined by consequences of highly stressful and morally-laden experiences, is poorly understood. Therefore, the objective of this study was to examine determinants of MI in Canadian Armed Forces (CAF) personnel. Methods: Data were obtained from the 2018 Canadian Armed Forces Members and Veterans Mental Health Follow-up Survey (CAFVMHS; unweighted n = 2,941). To identify military characteristics, sociodemographic variables, and deployment-related factors associated with increased levels of MI, a series of multiple linear regressions were conducted across deployed and non-deployed groups. Results: When all variables were considered among the deployed personnel, rank, experiencing military related sexual trauma, child maltreatment (i.e., physical abuse, emotional abuse and neglect), and stressful deployment experiences were significant predictors of increased MI total scores (β = 0.001 to β = 0.51, p &lt; 0.05). Feeling responsible for the death of an ally and inability to respond in a threatening situation were the strongest predictors of MI among stressful deployment experiences. Within the non-deployed sample, experiencing military-related or civilian sexual trauma and rank were significant predictors of increased MI total scores (β = 0.02 to β = 0.81, p &lt; 0.05). Conclusion: Exposure to stressful deployment experiences, particularly those involving moral-ethical challenges, sexual trauma, and childhood maltreatment were found to increase levels of MI in CAF personnel. These findings suggest several avenues of intervention, including education and policies aimed at mitigating sexual misconduct, as well as pre-deployment training to better prepare military personnel to deal effectively with morally injurious experiences.</p

Risk Factors for Moral Injury Among Canadian Armed Forces Personnel

Objectives: The traumatic nature of high-risk military deployment events, such as combat, is well-recognized. However, whether other service-related events and demographic factors increase the risk of moral injury (MI), which is defined by consequences of highly stressful and morally-laden experiences, is poorly understood. Therefore, the objective of this study was to examine determinants of MI in Canadian Armed Forces (CAF) personnel. Methods: Data were obtained from the 2018 Canadian Armed Forces Members and Veterans Mental Health Follow-up Survey (CAFVMHS; unweighted n = 2,941). To identify military characteristics, sociodemographic variables, and deployment-related factors associated with increased levels of MI, a series of multiple linear regressions were conducted across deployed and non-deployed groups. Results: When all variables were considered among the deployed personnel, rank, experiencing military related sexual trauma, child maltreatment (i.e., physical abuse, emotional abuse and neglect), and stressful deployment experiences were significant predictors of increased MI total scores (β = 0.001 to β = 0.51, p &lt; 0.05). Feeling responsible for the death of an ally and inability to respond in a threatening situation were the strongest predictors of MI among stressful deployment experiences. Within the non-deployed sample, experiencing military-related or civilian sexual trauma and rank were significant predictors of increased MI total scores (β = 0.02 to β = 0.81, p &lt; 0.05). Conclusion: Exposure to stressful deployment experiences, particularly those involving moral-ethical challenges, sexual trauma, and childhood maltreatment were found to increase levels of MI in CAF personnel. These findings suggest several avenues of intervention, including education and policies aimed at mitigating sexual misconduct, as well as pre-deployment training to better prepare military personnel to deal effectively with morally injurious experiences.</p

Moral injury associated with increased odds of past-year mental health disorders: a Canadian Armed Forces examination

Background: Potentially morally injurious experiences (PMIEs) are common during military service. However, it is unclear to what extent PMIEs are related to well-established adverse mental health outcomes. Objective: The objective of this study was to use a population-based survey to determine the associations between moral injury endorsement and the presence of past-year mental health disorders in Canadian Armed Forces (CAF) personnel and Veterans. Methods: Data were obtained from the 2018 Canadian Armed Forces Members and Veterans Mental Health Follow-up Survey (CAFVMHS). With a sample of 2,941 respondents, the weighted survey sample represented 18,120 active duty and 34,380 released CAF personnel. Multiple logistic regressions were used to assess the associations between sociodemographic characteristics (e.g. sex), military factors (e.g. rank), moral injury (using the Moral Injury Events Scale [MIES]) and the presence of specific mental health disorders (major depressive episode, generalized anxiety disorder, panic disorder, social anxiety disorder, PTSD, and suicidality). Results: While adjusting for selected sociodemographic and military factors, the odds of experiencing any past-year mental health disorder were 1.97 times greater (95% CI = 1.94–2.01) for each one-unit increase in total MIES score. Specifically, PTSD had 1.91 times greater odds (95% CI = 1.87–1.96) of being endorsed for every unit increase in MIES total score, while odds of past-year panic disorder or social anxiety were each 1.86 times greater (95% CI = 1.82–1.90) for every unit increase in total MIES score. All findings reported were statistically significant (p \u3c .001). Conclusion: These findings emphasize that PMIEs are robustly associated with the presence of adverse mental health outcomes among Canadian military personnel. The results of this project further underscore the necessity of addressing moral injury alongside other mental health concerns within the CAF

A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144