Observations of cosmic ray induced phosphenes

Phosphene observations by astronauts on flights near and far from earth atmosphere are discussed. It was concluded that phosphenes could be observed by the naked eye. Further investigation is proposed to determine realistic human tolerance levels for extended missions and to evaluate the need to provide special spacecraft shielding

(1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a \theta vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions used to regulate the infrared and treating the gauge field zero mode as a dynamical quantity. We find expressions for the degenerate vacuum states and construct the analog of the \theta vacuum. We then calculate the bilinear condensate in the model. We argue that the condensate does not affect the spectrum of the theory, although it is related to the string tension that characterizes the potential between fundamental test charges when the dynamical fermions are given a mass. We also argue that this result is fundamentally different from calculations that use periodicity conditions in x^1 as an infrared regulator.Comment: 20 pages, Revte

Quantum Mechanics of Dynamical Zero Mode in QCD1+1QCD_{1+1} on the Light-Cone

Motivated by the work of Kalloniatis, Pauli and Pinsky, we consider the theory of light-cone quantized $QCD_{1+1}$ on a spatial circle with periodic and anti-periodic boundary conditions on the gluon and quark fields respectively. This approach is based on Discretized Light-Cone Quantization (DLCQ). We investigate the canonical structures of the theory. We show that the traditional light-cone gauge $A_- = 0$ is not available and the zero mode (ZM) is a dynamical field, which might contribute to the vacuum structure nontrivially. We construct the full ground state of the system and obtain the Schr\"{o}dinger equation for ZM in a certain approximation. The results obtained here are compared to those of Kalloniatis et al. in a specific coupling region.Comment: 19 pages, LaTeX file, no figure

A Mathematical Model of Corneal Metabolism in the Presence of an Iris-Fixated Phakic Intraocular Lens

Purpose: Corneal endothelial cell loss is one of the possible complications associated with phakic iris-fixated intraocular lens (PIOL) implantation. We postulate that this might be connected to the alteration of corneal metabolism secondary to the lens implantation. Methods: A mathematical model of transport and consumption/production of metabolic species in the cornea is proposed, coupled with a model of aqueous flow and transport of metabolic species in the anterior chamber. Results: Results are presented both for open and closed eyelids. We showed that, in the presence of a PIOL, glucose availability at the corneal endothelium decreases significantly during sleeping. Conclusions: Implantation of a PIOL significantly affects nutrient transport processes to the corneal endothelium especially during sleep. It must still be verified whether this finding has a clinical relevance

Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front

We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by reviewing the known light-front solution of the Schwinger model, highlighting the issues that are relevant for reproducing the $\theta$-structure of the vacuum. The most important of these are the need to introduce degrees of freedom initialized on two different null planes, the proper incorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regulating singular operator products in a gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)$/Z_2$, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a $\theta$ vacuum. We formulate the model using periodicity conditions in $x^\pm$ for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected $Z_2$ vacuum structure, and verify that the discrete vacuum angle which enters has no effect on the spectrum of the theory. We then calculate the chiral condensate, which is sensitive to the vacuum structure. The result is nonzero, but inversely proportional to the periodicity length, a situation which is familiar from the Schwinger model. The origin of this behavior is discussed.Comment: 29 pages, uses RevTeX. Improved discussion of the physical subspace generally and the vacuum states in particular. Basic conclusions are unchanged, but some specific results are modifie

Shearlets and Optimally Sparse Approximations

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data", Birkh\"auser-Springe

Spectral simplicity and asymptotic separation of variables

We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean space (constant curvature space form) each eigenspace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure

Lyapunov exponent of the random Schr\"{o}dinger operator with short-range correlated noise potential

We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov exponent $\gamma$ which we determine explicitly as a function of the noise intensity \sigma and the frequency \omega. We find uniform two-parameter asymptotic expressions for $\gamma$ which allow us to evaluate $\gamma$ for different relations between \sigma and \omega. The value of the Lyapunov exponent is also obtained in the case of a short-range correlated noise, which is shown to be less than its white noise counterpart.Comment: 20 pages, 4 figure