Collision operator including large-angle scattering for moderately coupled plasma

A new approach has been developed to treat the large-angle as well as the small-angle binary collisions in high temperature and high density plasmas when the test particle distribution function f_α is even function about the test velocity and the relations of the mass and the velocity between the test particles and the field particles are satisfied with m_αm_β (such as electron–ion collision or Lorentz-gas model) and . With the approach, the Boltzmann collision operator is derived to be suitable for the plasma considered as weakly coupled (Coulomb logarithm ) and moderately coupled , i.e., for the electron–ion coupling constant Γ_ei<0.1. The modified collision operator has a direct and practical connection to the Rosenbluth potentials, the new reduced electron–ion collision operator differs from the original Fokker–Planck operator for Coulomb collisions by terms of order . Moreover, some calculations of relaxation rate and transport properties are given for new reduced electron–ion collision operator that shows corrections.     

Spontaneous bending of pre-stretched bilayers

We discuss spontaneously bent configurations of pre-stretched bilayer sheets that can be obtained by tuning the pre-stretches in the two layers. The two-dimensional nonlinear plate model we use for this purpose is an adaptation of the one recently obtained for thin sheets of nematic elastomers, by means of a rigorous dimensional reduction argument based on the theory of Gamma-convergence (Agostiniani and DeSimone in Meccanica. doi: 10.1007/s11012-017-0630-4, 2017, Math Mech Solids. doi: 10.1177/1081286517699991, arXiv:1509.07003, 2017). We argue that pre-stretched bilayer sheets provide us with an interesting model system to study shape programming and morphing of surfaces in other, more complex systems, where spontaneous deformations are induced by swelling due to the absorption of a liquid, phase transformations, thermal or electro-magnetic stimuli. These include bio-mimetic structures inspired by biological systems from both the plant and the animal kingdoms.     

Integrable $${\varvec{}}$$-dimensional systems with rational Lax pairs

The search for new integrable \((3+1)\)-dimensional partial differential systems is among the most important challenges in the modern integrability theory. It turns out that such a system can be associated with any pair of rational functions of one variable in general position, as established below using contact Lax pairs introduced in Sergyeyev (Lett Math Phys, 2017.  https://doi.org/10.1007/s11005-017-1013-4, arXiv:1401.2122).     

Regularity criteria for the 3D MHD equations in terms of the pressure

In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition b being in the Serrin's regularity class, if the pressure p belongs to L^α,γ with or the gradient field of pressure p belongs to L^α,γ with on [0,T], then the solution remains smooth on [0,T].     

Explicit conditions for the existence of exceptional body waves and subsonic surface waves in anisotropic elastic solids

It is known that a subsonic surface (Rayleigh) wave exists in an anisotropic elastic half-space x₂  0 if the first transonic state is not of Type 1. If the first transonic state is of Type 1 but the limiting wave is not exceptional, a subsonic surface wave exists. If the first transonic state is of Type 1 and the limiting wave is exceptional, a subsonic surface wave exists when . It is shown that an exceptional body wave is necessarily an exceptional transonic wave, and could be an exceptional limiting wave. Only two wave speeds are possible for an exceptional body wave. We present explicit conditions in terms of the reduced elastic compliances for the existence of an exceptional body wave. If an exceptional body wave exists, conditions are given for identifying whether the transonic state is of Type 1. Hence, through the existence of an exceptional body wave we provide explicit conditions for the existence of a subsonic surface wave with the exception when needs to be computed.     

Branch Switching from Coincident Bifurcation Points*

The definition of the solution set of a general non-linear structural problem depending on one external parameter is considered. Path-following techniques and singular point locating and identifying methods are reviewed, followed by so-called branch-switching methods used to detect secondary equilibrium paths associated with m-fold bifurcation points. Two methods introduced by Keller [[1] Keller, H. B. 1977. “Numerical solution of bifurcation and nonlinear eigenvalue problems”. In Applications of Bifurcation Theory Edited by: Rabinowitz, P. New York: Academic Press.  [Google Scholar]] and Kearfott [[2] Kearfott, R. B. 1983. Some general bifurcation techniques. SIAM J. Sci. Stat. Comput., 4: 52–68.  [Google Scholar]] are considered, and their performance when used together with the non-linear finite element method is verified.     

Some exact analytical solutions in structural optimization

In this article, the isoperimetric inequalities arising in exactly solvable structural optimization problems of stability are discussed. The purpose of this article is to review some types of inequalities that may be regarded as “isoperimetric.” This type of inequalities is long known in geometry and physics; see, e.g., Polya and Szegö (1951 Polya, G., Szegö, G. (1951). Isoperimetric Inequalities in Mathematical Physics. Princeton: Princeton University Press.[Crossref] [Google Scholar]), Banichuk (1977 Banichuk, N. V. (1977). Optimality conditions in the problem of elastic stress concentration. Journal of Applied Mathematics and Mechanics 41:920–925.[Crossref], [Web of Science ®] [Google Scholar]), Bandle (1980 Bandle, C. (1980). Isoperimetric Inequalities and Applications. Boston: Pitman. [Google Scholar]), and Chavel (2001 Chavel, I. (2001). Isoperimetric Inequalities Differential Geometric and Analytic Perspectives. Cambridge: Cambridge University Press. [Google Scholar]). The variational method is a powerful way to prove inequalities for systems described by ordinary differential equations. The proof of isoperimetric inequalities exploits the variational method and the Hölder inequality. The applications of this method for stability problems are illustrated in this article. The inequalities for Euler's column with boundary conditions of mixed type, for a twisted rod with periodic simple supports, and for a ring acted upon by a uniformly distributed, compressive hydrostatic load are rigorously verified.     

DYNAMIC PLASTIC BEHAVIOR OF A FREE-ROTATING HINGED BEAM STRIKING A CANTILEVER BEAM*

A study was made of the dynamic plastic response of two deformable beams colliding with each other. The driving beam, which was a free-rotating hinged beam with a tip mass at the free end, strikes at the tip mass of a target cantilever beam, which was stationary. Complete solutions based on the rigid, perfectly plastic material idealization were obtained for various deformation mechanisms during the dynamic response process of the two plastic beams. Typical numerical examples are presented to demonstrate [[1] Symonds, P. S. 1967. “Survey of Methods of Analysis for Plastic Deformation of Structure Under Dynamic Loading”. In Division of Engineering Report BU/NSRDC/ 1–67. Providence, RI: Brown University.  [Google Scholar]] the dynamic plastic behavior of the system after collision between two rectangular beams, as well as between an Ishaped beam and a rectangular beam; and [[2] Symonds, P. S. and Frye, C. W.G. 1988. On the Relation Between Rigid-Plastic and Elastic-Plastic Predictions of Response to Pulse Loading. Int. J. Impact Eng., 7: 139–149.  [Google Scholar]] the influence of the tip mass ratio on the plastic deformation of the driving and target beams.

     

The R-γ transition prediction model

The R_t turbulence closure (Goldberg 2003 Goldberg, U. 2003. “Turbulence Closure with a Topography-parameter-free Single Equation Model.” IJCFD 17 (1): 27–38.[Web of Science ®] , [Google Scholar]) is coupled with an intermittency transport equation, γ, to enable prediction of laminar-to-turbulent flow by-pass transition. The model is not correlation-based and is completely topography-parameter-free, thus ready for use in parallelized Computational Fluid Dynamics (CFD) solvers based on unstructured book-keeping. Several examples compare the R-γ model's performance with experimental data and with predictions by the Langtry–Menter γ-Re_θ transition closure (2009) Langtry, R.B., and F.R. Menter. 2009. “Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes.” AIAA J 47 (12): 2894–2906.[Crossref] , [Google Scholar]. Like the latter, the R-γ model is very sensitive to freestream turbulence levels, limiting its utility for engineering purposes.     

Natural convection in a vertical plane channel: DNS results for high Grashof numbers

The turbulent natural convection of a gas (Pr = 0.71) between two vertical infinite walls at different but constant temperatures is investigated by means of direct numerical simulation for a wide range of Grashof numbers (6.0 × 10⁶ > Gr > 1.0 × 10³). The maximum Grashof number is almost one order of magnitude higher than those of computations reported in the literature so far. Results for the turbulent transport equations are presented and compared to previous studies with special attention to the study of Verteegh and Nieuwstadt (Int J Heat Fluid Flow 19:135–149, 1998). All turbulence statistics are available on the TUHH homepage (http://www.tu-harburg.de/tt/dnsdatabase/dbindex.en.html). Accuracy considerations are based on the time averaged balance equations for kinetic and thermal energy. With the second law of thermodynamics Nusselt numbers can be determined by evaluating time averaged wall temperature gradients as well as by a volumetric time averaged integration. Comparing the results of both approaches leads to a direct measure of the physical consistency.