Ultrafast magnetophotoconductivity of semi-insulating gallium arsenide

The speed of opto-electronic switches is increased or decreased by the application of a magnetic field. This is achieved by inducing a carrier drift toward or away from the semiconductor surface, resulting in the enhancement or suppression of surface recombination. We establish that surface recombination plays a major role in determining the speed of the opto-electronic switch

Polymer-nanoparticle interactions in supramolecular hydrogels: Enabling long- term antibody delivery

Antibody drugs are a rapidly growing set of therapeutics that increasingly prove effective for clinical applications spanning from macular degeneration treatments, to targeted cancer therapies, and to passive immunization. These antibody treatments can be engineered to target almost any cell surface moiety and their production has since been scaled to an industrial level. Despite these advances, parenteral administration of antibodies is severely constrained by high viscosities at desirable doses, poor long-term antibody stability, high required frequency of administration, and therapeutically suboptimal pharmacokinetics. Herein, we demonstrate the development of supramolecular polymer-nanoparticle (PNP) interactions between poly(ethylene glycol)-poly(lactic acid) block copolymer nanoparticles (PEG-PLA) and modified hydroxypropylmethylcellulose (HPMC-x) polymers to engineer shear-thinning, self-healing hydrogels capable of stabilizing and delivering high concentrations of antibodies over prolonged timeframes (Figure 1). The PNP interactions underpinning the behavior of these materials afford injectability and tunable mechanical properties, while also controlling antibody release kinetics. In this work, we investigate how the thermodynamics of the PNP interaction affect in vitro and in vivo antibody release kinetics, pharmacokinetics, and bioavailability. Analysis of PEG-PLA surface density, HPMC-x hydrophobicity and modification extent, and hydrogel formulation reveal explicit design handles relating PNP thermodynamics to in vivo antibody release kinetics via subcutaneous injection. Differences in antibody release kinetics between in vitro and in vivo experiments were examined through mathematical modelling, revealing possible mechanisms of antibody uptake from subcutaneous space to the bloodstream when compared to literature. Overall, this work presents a robust set of design parameters to tune PNP interactions to develop a new nanotechnology-based platform for long-term, controlled antibody delivery. Please click Additional Files below to see the full abstract

Eigenfunctions decay for magnetic pseudodifferential operators

We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential operators (studied in \cite{IMP1}). This class contains the relativistic Schr\"{o}dinger operator with magnetic field

A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian

A two-dimensional Schr\"odinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call the set of eigenvalues near the $n$'th Landau level an $n$'th eigenvalue cluster, and study the distribution of eigenvalues in the $n$'th cluster as $n\to\infty$. A complete asymptotic expansion for the eigenvalue moments in the $n$'th cluster is obtained and some coefficients of this expansion are computed. A trace formula involving the first eigenvalue moments is obtained.Comment: 23 page

Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively in single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier along the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.Comment: 4 pages, 4 figure

Motion of Isolated bodies

It is shown that sufficiently smooth initial data for the Einstein-dust or the Einstein-Maxwell-dust equations with non-negative density of compact support develop into solutions representing isolated bodies in the sense that the matter field has spatially compact support and is embedded in an exterior vacuum solution

Separation of variables in perturbed cylinders

We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-to-one mapped onto a cylinder (rectangle or infinite strip). As a result of this transformation the original eigenvalue problem is reduced to an equivalent problem for an operator with variable coefficients. Taking advantage of the simple geometry we separate variables by means of the Fourier decomposition method. The ODE system obtained in this way is then solved numerically yielding the eigenvalues of the operator. The same approach allows us to find complex resonances arising in some non-compact domains. We discuss numerical examples related to quantum waveguide problems.Comment: LaTeX 2e, 18 pages, 6 figure

Morse homology for the heat flow

We use the heat flow on the loop space of a closed Riemannian manifold to construct an algebraic chain complex. The chain groups are generated by perturbed closed geodesics. The boundary operator is defined in the spirit of Floer theory by counting, modulo time shift, heat flow trajectories that converge asymptotically to nondegenerate closed geodesics of Morse index difference one.Comment: 89 pages, 3 figure