Boundary value problems of elasticity theory for plane domains with one-dimensional elastic reinforcements

This article is a translation of an article published in Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No 1, pp 103-114 Jan-Feb 1991.Many authors have examined problems related to the load transmission from an elastic rod to an elastic plane. It was assumed in the majority of investigationa that the stringer is a thin rectilinear rod transmitting only longitudinal forces while the rod contact with the plane is realized along a line. different modifications of sheet contact with a rectilinear tensile stringer considered as an inner stringer of finite length or as an infinite edge stringer were analyzed in [1, 2]. Problems about the reinforcement of holes in a plate by a thin rod of constant section that possesses bending and longitudinal stiffnesses were solved in [3]. The eccentricity of the connection between the shell middle surface and the rod was taken into account in [4] in a study of shells reinforced by thin curvilinear rods. Other models of the one-dimensional element connected to an elastic medium without taking account of its bending stiffness were analyzed in [5, 6]. Solutions of a number of problems with circular reinforcing elements are obtained in [7]. An isotropic finite or infinite, linearly elastic plate reinforced along part or all of the boundary and along certain internal lines by elastic curvilinear rods possessing variable longitudinal and bending stiffnesses, variable curvature and thickness, the eccentricity of the connection to the plate and with an arbitrary transverse section shape symmetric relative to the plate middle surface are studied in this paper. Boundary conditions on the line of plate contact with the inner or edge elastic rods are obtained for the reinforcement models generalizing [1, 2] by using the theory of elastic rods in the case of a plane state of stress. Existence and uniqueness theorems are proved for appropriate boundary value problems; the singularity of the stresses at angles and tips of the rods are proved. The relationships obtained carry over completely to the plane strain problem for an elastic cylinder reinforced by homogeneous cylindrical shells along the generator. Some of the results described here are represented in [8]

Global W2,pW^{2,p} estimates for solutions to the linearized Monge--Amp\`ere equations

In this paper, we establish global $W^{2,p}$ estimates for solutions to the linearized Monge-Amp\`ere equations under natural assumptions on the domain, Monge-Amp\`ere measures and boundary data. Our estimates are affine invariant analogues of the global $W^{2,p}$ estimates of Winter for fully nonlinear, uniformly elliptic equations, and also linearized counterparts of Savin's global $W^{2,p}$ estimates for the Monge-Amp\`ere equations.Comment: v2: presentation improve

Vector Meson Production in Ultraperipheral Heavy Ion Collisions

The ultraperipheral heavy ion collisions (UPC's) are an important alternative to study the QCD dynamics until the next generation of $e^+e^-/ ep / eA$ colliders become reality. Due to the coherent action of all the protons in the nucleus, the electromagnetic field is very strong and the resulting flux of equivalent photons is large, which allows to study two-photon as well as photonuclear interactions at high energies. In this paper we present a brief review of the vector meson production in UPC's at high energies using the QCD color dipole approach to describe their photonuclear production and the perturbative QCD Pomeron (BFKL dynamics) to describe the double meson production in photon-photon process. Predictions for rates and integrated cross sections are presented for energies of RHIC and LHC.Comment: 16 pages, 1 figure. Version to be published in Journal of Physics G: Nuclear and Particle Physic

Gay, Mostly Gay, or Bisexual Leaning Gay? An Exploratory Study Distinguishing Gay Sexual Orientations Among Young Men

This exploratory study assessed physiological, behavioral, and self-report measures of sexual and romantic indicators of sexual orientation identities among young men (mean age = 21.9 years) with predominant same-sex sexual and romantic interests: those who described themselves as bisexual leaning gay (n = 11), mostly gay (n = 17), and gay (n = 47). Although they were not significantly distinguishable based on physiological (pupil dilation) responses to nude stimuli, on behavioral and self-report measures a descending linear trend toward the less preferred sex (female) was significant regarding sexual attraction, fantasy, genital contact, infatuation, romantic relationship, sex appeal, and gazing time to the porn stimuli. Results supported a continuum of sexuality with distinct subgroups only for the self-report measure of sexual attraction. The other behavioral and self-report measures followed the same trend but did not significantly differ between the bisexual leaning gay and mostly gay groups, likely the result of small sample size. Results suggest that romantic indicators are as good as sexual measures in assessing sexual orientation and that a succession of logically following groups from bisexual leaning gay, mostly gay, to gay. Whether these three groups are discrete or overlapping needs further research

Neutrally reinforced holes in symmetrically laminated plates

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76616/1/AIAA-46360-396.pd

Computation of the temperature dependence of the heat capacity of complex molecular systems using random color noise

We propose a new method for computing the temperature dependence of the heat capacity in complex molecular systems. The proposed scheme is based on the use of the Langevin equation with low frequency color noise. We obtain the temperature dependence of the correlation time of random noises, which enables to model the partial thermalization of high-frequency vibrations, which is a pure quantum effect. By applying the method to carbon nanotubes, we show that the consideration of the color noise in the Langevin equation allows to reproduce the temperature evolution of the specific heat with good accuracy.Comment: 11 pages, 5 figure

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande

On the structure of phase transition maps for three or more coexisting phases

This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented here is an expanded version of that lecture.Comment: 23 pages, 6 figure

Existence, uniqueness and structure of second order absolute minimisers

Let ⊆ Rn be a bounded open C1,1 set. In this paper we prove the existence of a unique second order absolute minimiser u∞ of the functional E∞(u, O) := F(·, u)L∞(O), O ⊆ measurable, with prescribed boundary conditions for u and Du on ∂ and under natural assumptions on F. We also show that u∞ is partially smooth and there exists a harmonic function f∞ ∈ L1() such that F(x, u∞(x)) = e∞ sgn f∞(x) for all x ∈ { f∞ = 0}, where e∞ is the infimum of the global energy