Temporal Distributional Limit Theorems for Dynamical Systems

Suppose \(\{T^t\}\) is a Borel flow on a complete separable metric space X, \(f:X\rightarrow \mathbb R\) is Borel, and \(x\in X\). A temporal distributional limit theorem is a scaling limit for the distributions of the random variables \(X_T:=\int _0^t f(T^s x)ds\), where t is chosen randomly uniformly from [0, T], x is fixed, and \(T\rightarrow \infty \). We discuss such laws for irrational rotations, Anosov flows, and horocycle flows.     

Non-Gibbsian stochastic light-mode dynamics of passive mode locking

We study a stochastic light-mode system with non-Gibbsian steady state statistics, unravelling global nonequilibrium phase transition properties. It relates to the onset of passive mode-locking in the general case of lasers with arbitrary dispersion and Kerr nonlinearity that includes the nonsolitonic regime. The solution is facilitated by a special stationarity criterion imposed by the system gain balance. We show that the mode-locking phase transition is generic, and give exact expressions for the pulse power and its stability map. We find that at the boundary of the mode-locking stability the pulse power is exactly one half of the total intracavity power, and that the parameter region for the most resistant pulses against noise destabilization is not at the soliton condition.     

Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts

We find a necessary and sufficient condition for the Ruelle operator of a weakly Hölder continuous potential on a topologically mixing countable Markov shift to act with spectral gap on some rich Banach space. We show that the set of potentials satisfying this condition is open and dense for a variety of topologies. We then analyze the complement of this set (in a finer topology) and show that among the three known obstructions to spectral gap (weak positive recurrence, null recurrence, transience), transience is open and dense, and null recurrence and weak positive recurrence have empty interior.     

Symmetry breaking in honeycomb photonic lattices

We study the phenomena associated with symmetry breaking in honeycomb photonic lattices. As the honeycomb structure is gradually deformed, conical diffraction around its diabolic points becomes elliptic and eventually no longer occurs. As the deformation is further increased, a gap opens between the first two bands, and the lattice can support a gap soliton. The existence of the gap soliton serves as a means to detect the symmetry breaking and provide an estimate of the size of the gap.     

Microscopical investigations of nisin-loaded nanoliposomes prepared by Mozafari method and their bacterial targeting

Nanoencapsulation may improve activity of protein or polypeptide antimicrobials against a variety of microorganisms. In this study, nanoliposomes prepared from different lipids (Phospholipon 90H, Phospholipon 100H, dipalmitoylphosphatidylcholine (DPPC), stearylamine (SA), dicetyl phosphate (DCP) and cholesterol) by a new, non-toxic and scalable method, were tested for their capacity to encapsulate nisin Z and target bacteria (Bacillus subtilis and Pseudomonas aeruginosa). Factors affecting the entrapment efficiency (charge and cholesterol concentration in the vesicles) and stability of nanoliposomes were assessed. The nanoliposomes and their bacterial targeting were visualised, using different microscopes under air and liquid environments. Nisin was entrapped in different nanoliposomes with encapsulation efficiencies (EE) ranging from 12% to 54%. Anionic vesicles possessed the highest EE for nisin while increase in cholesterol content in lipid membranes up to 20% molar ratio resulted in a reduction in EE. Stability of nanoliposome-encapsulated nisin was demonstrated for at least 14 months at 4 °C (DPPC:DCP:CHOL vesicles) and for 12 months at 25 °C (DPPC:SA:CHOL vesicles).     

Phase Transitions for Countable Markov Shifts

We study the analyticity of the topological pressure for some one-parameter families of potentials on countable Markov shifts. We relate the non-analyticity of the pressure to changes in the recurrence properties of the system. We give sufficient conditions for such changes to exist and not to exist. We apply these results to the Manneville–Pomeau map, and use them to construct examples with different critical behavior. Received: 6 March 2000 / Accepted: 17 October 2000     

Sono-activation of persulfate by Fe-expanded perlite catalyst for oxidative degradation of Orange G: synergy study,influence of parameters and phytotoxicity tests

Research on Chemical Intermediates - Iron-coated expanded perlite (Fe-EP) was prepared as a heterogeneous catalyst for activating persulfate (PS) to degrade Orange G (OG) under ultrasonic...     

Efficient Removal Lemmas for Matrices

Order - It was recently proved in Alon et al. (2017) that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with...     

Observation of asymptotic localization of a wave packet

We present the experimental observation of asymptotic localization, a new regime of wave packet localization under the action of an external linear potential gradient. We employ arrays of evanescently coupled waveguides and directly observe the wave packet trajectory, which exhibits an oscillation with vanishing amplitude and period.