Development of singularities for the compressible Euler equations with external force in several dimensions

We consider solutions to the Euler equations in the whole space from a certain class, which can be characterized, in particular, by finiteness of mass, total energy and momentum. We prove that for a large class of right-hand sides, including the viscous term, such solutions, no matter how smooth initially, develop a singularity within a finite time. We find a sufficient condition for the singularity formation, "the best sufficient condition", in the sense that one can explicitly construct a global in time smooth solution for which this condition is not satisfied "arbitrary little". Also compactly supported perturbation of nontrivial constant state is considered. We generalize the known theorem by Sideris on initial data resulting in singularities. Finally, we investigate the influence of frictional damping and rotation on the singularity formation.Comment: 23 page

Generalized momenta of mass and their applications to the flow of compressible fluid

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.Comment: 10 pages, Proceedings of the International Conference on Hyperbolic Problems, Lyon, 2006, France. In pres

Nonlinear effects in tunnelling escape in N-body quantum systems

We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum equations of the multiparticle system we find the tunneling rate and time evolutions of the number of trapped particles for different nonlinearity values.Comment: 10 pages, 3 figure

Formation of singularities in solutions to ideal hydrodynamics of freely cooling inelastic gases

We consider solutions to the hyperbolic system of equations of ideal granular hydrodynamics with conserved mass, total energy and finite momentum of inertia and prove that these solutions generically lose the initial smoothness within a finite time in any space dimension $n$ for the adiabatic index $\gamma \le 1+\frac{2}{n}.$ Further, in the one-dimensional case we introduce a solution depending only on the spatial coordinate outside of a ball containing the origin and prove that this solution under rather general assumptions on initial data cannot be global in time too. Then we construct an exact axially symmetric solution with separable time and space variables having a strong singularity in the density component beginning from the initial moment of time, whereas other components of solution are initially continuous.Comment: 13 pages, 3 figure

On the existence of chaos for the viscous van Wijngaarden-Eringen equation

This is the author’s version of a work that was accepted for publication in Chaos, Solitons and Fractals. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Chaos, Solitons and Fractals 89 (2016) 100–104. DOI 10.1016/j.chaos.2015.10.009.We study the viscous van Wijngaarden–Eringen equation: ∂2u ∂t2 − ∂2u ∂x2 = (Red)−1 ∂3u ∂t∂x2 + a2 0 ∂4u ∂t2∂x2 (1) which corresponds to the linearized version of the equation that models the acoustic planar propagation in bubbly liquids. We show the existence of an explicit range, solely in terms of the constants a0 and Red, in which we can ensure that this equation admits a uniformly continuous, Devaney chaotic and topologically mixing semigroup on Herzog’s type Banach spaces. © 2015 Elsevier Ltd. All rights reserved.Conejero Casares, JA.; Lizama, C.; Murillo Arcila, M. (2016). On the existence of chaos for the viscous van Wijngaarden-Eringen equation. Chaos, Solitons and Fractals. 89:100-104. doi:10.1016/j.chaos.2015.10.009S1001048

Blowup Criterion for the Compressible Flows with Vacuum States

We prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth(strong) solutions for the 3-dimensional compressible Navier-Stokes equations, which will happen, for example, if the initial density is compactly supported \cite{X1}. More precisely, if a solution of the compressible Navier-Stokes equations is initially regular and loses its regularity at some later time, then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches. Our result is the same as Ponce's criterion for 3-dimensional incompressible Euler equations (\cite{po}). Moreover, our method can be generalized to the full Compressible Navier-Stokes system which improve the previous results. In addition, initial vacuum states are allowed in our cases.Comment: 17 page

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

EnnCore: End-to-End Conceptual Guarding of Neural Architectures

The EnnCore project addresses the fundamental security problem of guaranteeing safety, transparency, and robustness in neural-based architectures. Specifically, EnnCore aims at enabling system designers to specify essential conceptual/behavioral properties of neural-based systems, verify them, and thus safeguard the system against unpredictable behavior and attacks. In this respect, EnnCore will pioneer the dialogue between contemporary explainable neural models and full-stack neural software verification. This paper describes existing studies' limitations, our research objectives, current achievements, and future trends towards this goal. In particular, we describe the development and evaluation of new methods, algorithms, and tools to achieve fully-verifiable intelligent systems, which are explainable, whose correct behavior is guaranteed, and robust against attacks. We also describe how EnnCore will be validated on two diverse and high-impact application scenarios: securing an AI system for (i) cancer diagnosis and (ii) energy demand response

Citric acid wastewater as electron donor for biological sulfate reduction

Citrate-containing wastewater is used as electron donor for sulfate reduction in a biological treatment plant for the removal of sulfate. The pathway of citrate conversion coupled to sulfate reduction and the microorganisms involved were investigated. Citrate was not a direct electron donor for the sulfate-reducing bacteria. Instead, citrate was fermented to mainly acetate and formate. These fermentation products served as electron donors for the sulfate-reducing bacteria. Sulfate reduction activities of the reactor biomass with acetate and formate were sufficiently high to explain the sulfate reduction rates that are required for the process. Two citrate-fermenting bacteria were isolated. Strain R210 was closest related to Trichococcus pasteurii (99.5% ribosomal RNA (rRNA) gene sequence similarity). The closest relative of strain S101 was Veillonella montepellierensis with an rRNA gene sequence similarity of 96.7%. Both strains had a complementary substrate range

Loneliness of Older Immigrant Groups in Canada: Effects of Ethnic-Cultural Background

This study aimed to explore the loneliness of several groups of older immigrants in Canadacompared to native-born older adults. Data from the Canadian General Social Survey, Cycle 22 (Nolder adults = 3,692) were used. The dependent variable is the 6 item De Jong Gierveld lonelinessscale. Determinants of loneliness included country of birth, ethnic background (cultural context);belongingness (community context) and social networks (social context). Results showed that onlysome immigrant groups are significantly lonelier than older adults born in Canada. Immigrants withsimilar language and culture are not lonelier; while those from countries that differ in nativelanguage/culture are significantly higher on loneliness. Multivariate analyses showed the importanceof cultural background, of composition of the network of relatives and friends, and of localparticipation and feelings of belonging to the Canadian society in explaining loneliness of olderimmigrants