Geometric analysis of optical frequency conversion and its control in quadratic nonlinear media

We analyze frequency conversion and its control among three light waves using a geometric approach that enables the dynamics of the waves to be visualized on a closed surface in three dimensions. It extends the analysis based on the undepleted-pump linearization and provides a simple way to understand the fully nonlinear dynamics. The Poincaré sphere has been used in the same way to visualize polarization dynamics. A geometric understanding of control strategies that enhance energy transfer among interacting waves is introduced, and the quasi-phase-matching strategy that uses microstructured quadratic materials is illustrated in this setting for both type I and II second-harmonic generation and for parametric three-wave interactions

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures

Locked and Unlocked Polygonal Chains in 3D

In this paper, we study movements of simple polygonal chains in 3D. We say that an open, simple polygonal chain can be straightened if it can be continuously reconfigured to a straight sequence of segments in such a manner that both the length of each link and the simplicity of the chain are maintained throughout the movement. The analogous concept for closed chains is convexification: reconfiguration to a planar convex polygon. Chains that cannot be straightened or convexified are called locked. While there are open chains in 3D that are locked, we show that if an open chain has a simple orthogonal projection onto some plane, it can be straightened. For closed chains, we show that there are unknotted but locked closed chains, and we provide an algorithm for convexifying a planar simple polygon in 3D with a polynomial number of moves.Comment: To appear in Proc. 10th ACM-SIAM Sympos. Discrete Algorithms, Jan. 199

Dynamical density functional theory for the dewetting of evaporating thin films of nanoparticle suspensions exhibiting pattern formation

Recent experiments have shown that the striking structure formation in dewetting films of evaporating colloidal nanoparticle suspensions occurs in an ultrathin `postcursor' layer that is left behind by a mesoscopic dewetting front. Various phase change and transport processes occur in the postcursor layer, that may lead to nanoparticle deposits in the form of labyrinthine, network or strongly branched `finger' structures. We develop a versatile dynamical density functional theory to model this system which captures all these structures and may be employed to investigate the influence of evaporation/condensation, nanoparticle transport and solute transport in a differentiated way. We highlight, in particular, the influence of the subtle interplay of decomposition in the layer and contact line motion on the observed particle-induced transverse instability of the dewetting front.Comment: 5 pages, 5 figure

Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

Holography and Cosmological Singularities

Certain null singularities in ten dimensional supergravity have natural holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT correspondence. In many situations the holographic duals appear to be well defined in regions where the supergravity develops singularities. We describe some recent progress in this area.Comment: Anomaly equation corrected. References adde

Radiation Nephropathy: A Review

The marked radiosensitivity of renal tissue represents a limitation on the total radiotherapeutic dose that safely can be applied to treatment volumes that include the kidneys. Radiation nephropathy is characterized by a progressive reduction in renal hemodynamics associated with a severe anemia. The latter is often normochromic normocytic in character, but can progress to a microangiopathic hemolytic anemia. The pathogenic mechanisms responsible for the development of radiation nephropathy remain ill-defined. Experimental studies which allow serial determinations of functional, morphologic, and cell kinetic radiation-induced changes indicate that primarily glomerular but also tubular alterations occur in the primary stages of radiation nephropathy. Glomerular capillary endothelial cell loss is seen within several weeks of irradiation. Remaining endothelial cells exhibit increased permeability leading to a subendothelial transudate. Mesangiolysis also is observed. In contrast, podocytes appear to be relatively unaffected at this stage. The endothelial changes appear to resolve, but the mesangial lesions progress, with hypercellularity and/or hypertrophy, increased mesangial matrix, mesangial sclerosis, and ultimately, glomerulosclerosis. These mesangial changes are similar to those observed in other chronic glomerulopathies. Dietary protein restriction, corticosteroids, and ACE-inhibitors all can reduce the severity of experimental radiation nephropathy

Impact Ionization in ZnS

The impact ionization rate and its orientation dependence in k space is calculated for ZnS. The numerical results indicate a strong correlation to the band structure. The use of a q-dependent screening function for the Coulomb interaction between conduction and valence electrons is found to be essential. A simple fit formula is presented for easy calculation of the energy dependent transition rate.Comment: 9 pages LaTeX file, 3 EPS-figures (use psfig.sty), accepted for publication in PRB as brief Report (LaTeX source replaces raw-postscript file