The asymmetric sandwich theorem

We discuss the asymmetric sandwich theorem, a generalization of the Hahn-Banach theorem. As applications, we derive various results on the existence of linear functionals that include bivariate, trivariate and quadrivariate generalizations of the Fenchel duality theorem. Most of the results are about affine functions defined on convex subsets of vector spaces, rather than linear functions defined on vector spaces. We consider both results that use a simple boundedness hypothesis (as in Rockafellar's version of the Fenchel duality theorem) and also results that use Baire's theorem (as in the Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper also contains some new results about metrizable topological vector spaces that are not necessarily locally convex.Comment: 17 page

Rock Response in a 12-M Tunnel through a Zone of Low Strength

At the Rocky Mountain Pumped Storage Project a 12 meter diameter power tunnel was excavated through sedimentary rock for 760 meters. Approximately 10% of this tunnel was through Pennington shale that is described as a dark gray massive organic shale. This paper will describe the methods of testing .and rock characterization, the results of instrumentation and monitoring, and the post-construction testing program for the excavation, and conclude with a discussion of the observed rock response in relation to the measured strength and deformation properties. This particular zone of the tunnel required the addition of longer rockbolts, and a discussion of that supplemental rock reinforcement will be included

Phase velocity and phase diffusion in periodically driven discrete state systems

We develop a theory to calculate the effective phase diffusion coefficient and the mean phase velocity in periodically driven stochastic models with two discrete states. This theory is applied to a dichotomically driven Markovian two state system. Explicit expressions for the mean phase velocity, the effective phase diffusion coefficient and the P\'eclet number are analytically calculated. The latter shows as a measure of phase-coherence forced synchronization of the stochastic system with respect to the periodic driving. In a second step the theory is applied to a non Markovian two state model modeling excitable systems. The results prove again stochastic synchronization to the periodic driving and are in good agreement with simulations of a stochastic FitzHugh-Nagumo system.Comment: 11 pages, 7 figure

Effect of the C-bridge length on the ultraviolet-resistance of oxycarbosilane low-k films

The ultra-violet (UV) and vacuum ultra-violet (VUV) resistance of bridging alkylene groups in organosilica films has been investigated. Similar to the Si-CH3 (methyl) bonds, the Si-CH2-Si (methylene) bonds are not affected by 5.6 eV irradiation. On the other hand, the concentration of the Si-CH2-CH2-Si (ethylene) groups decreases during such UV exposure. More significant difference in alkylene reduction is observed when the films are exposed to VUV (7.2 eV). The ethylene groups are depleted by more than 75% while only about 40% methylene and methyl groups loss is observed. The different sensitivity of bridging groups to VUV light should be taken into account during the development of curing and plasma etch processes of low-k materials based on periodic mesoporous organosilicas and oxycarbosilanes. The experimental results are qualitatively supported by ab-initio quantum-chemical calculations

Drift and Diffusion in Periodically Driven Renewal Processes

We consider the drift and diffusion properties of periodically driven renewal processes. These processes are defined by a periodically time dependent waiting time distribution, which governs the interval between subsequent events. We show that the growth of the cumulants of the number of events is asymptotically periodic and develop a theory which relates these periodic growth coefficients to the waiting time distribution defining the periodic renewal process. The first two coefficients, which are the mean frequency and effective diffusion coefficient of the number of events are considered in greater detail. They may be used to quantify stochastic synchronization.Comment: 29 pages, 6 figures, submitted to Journal of Statistical Physic

Stochastic resonance in a non Markovian discrete state model for excitable systems

We study a non Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable systems with periodical driving. In the limit of a small amplitude of the external signal we derive expressions for the spectral power amplification and the signal to noise ratio as well as for the inter-spike interval distribution.Comment: 5 pages, 3 figure

A stochastic flow rule for granular materials

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation

Mode-multiplexing deep-strong light-matter coupling

Dressing quantum states of matter with virtual photons can create exotic effects ranging from vacuum-field modified transport to polaritonic chemistry, and may drive strong squeezing or entanglement of light and matter modes. The established paradigm of cavity quantum electrodynamics focuses on resonant light-matter interaction to maximize the coupling strength $\Omega_\mathrm{R}/\omega_\mathrm{c}$, defined as the ratio of the vacuum Rabi frequency and the carrier frequency of light. Yet, the finite oscillator strength of a single electronic excitation sets a natural limit to $\Omega_\mathrm{R}/\omega_\mathrm{c}$. Here, we demonstrate a new regime of record-strong light-matter interaction which exploits the cooperative dipole moments of multiple, highly non-resonant magnetoplasmon modes specifically tailored by our metasurface. This multi-mode coupling creates an ultrabroadband spectrum of over 20 polaritons spanning 6 optical octaves, vacuum ground state populations exceeding 1 virtual excitation quantum for electronic and optical modes, and record coupling strengths equivalent to $\Omega_\mathrm{R}/\omega_\mathrm{c}=3.19$. The extreme interaction drives strongly subcycle exchange of vacuum energy between multiple bosonic modes akin to high-order nonlinearities otherwise reserved to strong-field physics, and entangles previously orthogonal electronic excitations solely via vacuum fluctuations of the common cavity mode. This offers avenues towards tailoring phase transitions by coupling otherwise non-interacting modes, merely by shaping the dielectric environment

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure