Duality and Hidden Symmetries in Interacting Particle Systems

In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is of SU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil its SU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess the SU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.     

Interface Energy in the Edwards-Anderson Model

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from −1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulates finite temperature systems and works with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension D _c =2.5. The results show a good agreement with the mean field theory predictions.     

Micro-Raman investigations of the formaldehyde-ice system

Rapidly frozen aqueous solutions containing variable amounts of dissolved formaldehyde (0.1, 5, 7, 10, 15, and 20 mol %) have been analyzed by micro-Raman spectroscopy at ambient pressure and low temperature. The importance of the formladehyde-ice system has been repeatedly quoted in various contexts, such as atmospheric and snowpack chemistry and interstellar and cometary ices. Understanding and characterizing the effects of freezing and the interactions of formaldehyde with ice are therefore of relevant interest. In this study, the distinct vibrational signatures of the oligomers present in the solution and in the frozen ice mixtures have been identified in the 120-4000 cm(-1) spectral range. From the subtle changes of the bands assigned to the CO and CH group frequencies, at least two distinct crystalline phases (pI and pII) are found to coexist with ice at different temperatures. Depending on the cooling-rewarming protocol, pI is found to crystallize in the 163-213 K temperature range. Above approximately 213 K, pI gets transformed irreversibly into pII which is stable up to approximately 234 K. pII is found to interact more strongly with ice than pI, as revealed, for example, by the drop in frequency of the bands assigned to the O-H stretching as pI transforms into pII. It is suggested that pII consists of a hydrogen-bonded network of oligomers and water molecules. On the other hand, it is suggested that the oligomers mainly present in pI interact through weak forces with the surrounding water molecules.     

Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser

We show the standard two-level continuous-time model of loss-modulated CO2 lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings. Our results suggest that the two-parameter space of class B laser models and that of a certain class of discrete mappings could be isomorphic.     

On the Rubin–Stark Conjecture for a special class of CM extensions of totally real number fields

We use Greithers recent results on Brumers Conjecture to prove Rubins integral version of Starks Conjecture, up to a power of 2, for an infinite class of CM extensions of totally real number fields, called nice extensions under the assumption that a certain Iwasawa –invariant vanishes. As a consequence and under the same assumption, we show that the Brumer–Stark Conjecture is true for nice extensions, up to a power of 2.Mathematical Subject Classification (1991): 11R42, 11R58, 11R27Research on this project was partially supported by NSF grants DMS–9801267 and DMS–0196340.in final form: 16 July 2003     

Universal statistics of the critical depinning force of elastic systems in random media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.     

Characterization of the time dependence of polarization mode dispersion

We elaborate on a recently proposed model of the temporal dependence of polarization mode dispersion in long fiber links. We evaluate the probability that a channel of a wavelength-division multiplexed system never incurs an outage, and the range of frequency over which the parameters that characterize the temporal statistics of the differential group delay are correlated.     

Two-phase channel structures based on alpha-cyclodextrin-polyethylene glycol inclusion complexes

Wide-angle X-ray scattering observations of alpha-cyclodextrin (CD)-poly(ethylene glycol) (PEG) inclusion complexes (ICs) have shown for the first time that two crystalline columnar modifications (forms I and II) are produced in the process of their formation. This was made possible by precise azimuthal X-ray diffraction scanning of oriented IC samples. Form I is characterized by CDs threaded onto PEG chains and arranged along channels in the order head-to-head/tail-to-tail, while form II is formed by unbound CDs also arranged into columns in a head-to-tail and also possibly a head-to-head/tail-to-tail manner, probably as a result of template crystallization on the form I IC crystals. It was shown that similar structural peculiarities are inherent for channel structures based on ICs obtained with PEG with a wide range of molecular weights (MWs). The characteristic feature of ICs based on PEG, especially with MW > 8000, is the presence of unbound polymer in the composition of the complex. The amount of unbound PEG was shown to rise with increasing MW of PEG, resulting in greater imperfections in the IC crystalline structure. The polyblock structure of ICs based on alpha-CD and PEG was therefore proposed.     

Edge-enhanced imaging with polyvinyl alcohol/acrylamide photopolymer gratings

We demonstrate edge-enhanced imaging produced by volume phase gratings recorded on a polyvinyl alcohol/acrylamide photopolymer. Bragg diffraction, exhibited by volume gratings, modifies the impulse response of the imaging system, facilitating spatial filtering operations with no need for a physical Fourier plane. We demonstrate that Kogelnik's coupled-wave theory can be used to calculate the transfer function for the transmitted and the diffracted orders. The experimental and simulated results agree, and they demonstrate the feasibility of our proposal.     

Geometric properties of the sections of solutions to the Monge-Ampère equation

In this paper we establish several geometric properties of the cross sections of generalized solutions to the Monge-Ampère equation , when the measure satisfies a doubling property. A main result is a characterization of the doubling measures in terms of a geometric property of the cross sections of . This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.