Self-adjoint sub-classes of generalized thin film equations

In this work we consider a class of fourth-order nonlinear partial differential equation containing several un-specified coefficient functions of the dependent variable which encapsulates various mathematical models used, e.g. for describing the dynamics of thin liquid films. We determine the subclasses of these equations which are self-adjoint. By using a general theorem on conservation laws proved by one of the authors (NHI) we find conservation laws for some of these partial differential equations without classical Lagrangians.     

Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication

We propose a numerical method to obtain the transient and first passage time distributions of first- and second-order Multi-Regime Markov Fluid Queues (MRMFQ). The method relies on the observation that these transient measures can be computed via the stationary analysis of an auxiliary MRMFQ. This auxiliary MRMFQ is constructed from the original one, using sample path arguments, and has a larger cardinality stemming from the need to keep track of time. The conventional method to approximately model the deterministic time horizon is Erlangization. As an alternative, we propose the so-called ME-fication technique, in which a Concentrated Matrix Exponential (CME) distribution replaces the Erlang distribution for approximating deterministic time horizons. ME-fication results in much lower state-space dimensionalities for the auxiliary MRMFQ than would be with Erlangization. Numerical results are presented to validate the effectiveness of ME-fication along with the proposed numerical method.

     

Investigations of polymer dynamics in nanoporous media by field cycling NMR relaxometry and the dipolar correlation effect

The chain dynamics of short-chain perfluoropolyether melts confined in Vycor nanoporous media has been characterized by field cycling nuclear magnetic resonance relaxometry and the dipolar correlation effect. The slowdown of motions under confinement, leading to larger residual dipolar couplings, has been probed by looking at the quotient of stimulated and primary echoes. Using field cycling relaxometry, it has been shown that there is strong evidence of reptation-like motion, even for such short-chain polymers as shown by the frequency and molecular weight dependences of the spin-lattice relaxation time.     

Spatiotemporal optical solitons in nonlinear dissipative media: from stationary light bullets to pulsating complexes

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation.     

Conservation laws and exact solutions for nonlinear diffusion in anisotropic media

Conservation laws and exact solutions of nonlinear differential equations describing diffusion phenomena in anisotropic media with external sources are constructed. The construction is based on the method of nonlinear self-adjointness. Numerous exact solutions are obtained by using the recent method of conservation laws. These solutions are different from group invariant solutions and can be useful for investigating diffusion phenomena in complex media, e.g. in oil industry.     

Quantized separations of phase-locked soliton pairs in fiber lasers

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.