Piezoviscous effects in nonconformal contacts lubricated hydrodynamically

The analysis is concerned with the piezoviscous-rigid regime of lubrication for the general case of elliptical contacts. In this regime several formulas of the lubricant film thickness have been proposed by Hamrock and Dowson, by Dowson et al., and more recently by Houpert. However, either they do not include the load parameter W, which has a strong effect on film thickness, or they overestimate the film thickness by using the Barus formula for pressure-viscosity characteristics. The Roelands formula was used for the pressure-viscosity relationship. The effects of the dimensionless load, speed, and materials parameters, the radius ratio, and the lubricant entrainment direction were investigated. The dimensionless load parameter was varied over a range of one order of magnitude. The dimensionless speed parameter was varied by 5.6 times the lowest value. Conditions corresponding to the use of solid materials of steel, bronze, and silicon nitride and lubricants of paraffinic and naphthenic mineral oil were considered in obtaining the exponent in the dimensionless materials parameter. The radius ratio was varied from 0.2 to 64 (a configuration approaching a line contact). Forty-one cases were used in obtaining a minimum film thickness formula. Contour plots indicate in detail the pressure developed between the contacting solids

Higher Order and boundary Scaling Fields in the Abelian Sandpile Model

The Abelian Sandpile Model (ASM) is a paradigm of self-organized criticality (SOC) which is related to $c=-2$ conformal field theory. The conformal fields corresponding to some height clusters have been suggested before. Here we derive the first corrections to such fields, in a field theoretical approach, when the lattice parameter is non-vanishing and consider them in the presence of a boundary.Comment: 7 pages, no figure

Boundary conditions and defect lines in the Abelian sandpile model

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.Comment: 8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev.

Height variables in the Abelian sandpile model: scaling fields and correlations

We compute the lattice 1-site probabilities, on the upper half-plane, of the four height variables in the two-dimensional Abelian sandpile model. We find their exact scaling form when the insertion point is far from the boundary, and when the boundary is either open or closed. Comparing with the predictions of a logarithmic conformal theory with central charge c=-2, we find a full compatibility with the following field assignments: the heights 2, 3 and 4 behave like (an unusual realization of) the logarithmic partner of a primary field with scaling dimension 2, the primary field itself being associated with the height 1 variable. Finite size corrections are also computed and successfully compared with numerical simulations. Relying on these field assignments, we formulate a conjecture for the scaling form of the lattice 2-point correlations of the height variables on the plane, which remain as yet unknown. The way conformal invariance is realized in this system points to a local field theory with c=-2 which is different from the triplet theory.Comment: 68 pages, 17 figures; v2: published version (minor corrections, one comment added

Vacancy localization in the square dimer model

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this formalism, we can address the question of the possible motion of the vacancy induced by dimer slidings. We find a probability 57/4-10Sqrt[2] for the vacancy to be strictly jammed in an infinite system. More generally, the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9/8. On a finite system, the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1/4. The resultant weak localization of vacancies still allows for unbounded diffusion, characterized by a diffusion exponent that we relate to that of diffusion on spanning trees. We also implement numerical simulations of the model with both free and periodic boundary conditions.Comment: 35 pages, 24 figures. Improved version with one added figure (figure 9), a shift s->s+1 in the definition of the tree size, and minor correction

Charge ordering in the spinels AlV2_2O4_4 and LiV2_2O4_4

We develop a microscopic theory for the charge ordering (CO) transitions in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$ (under pressure). The high degeneracy of CO states is lifted by a coupling to the rhombohedral lattice deformations which favors transition to a CO state with inequivalent V(1) and V(2) sites forming Kagom\'e and trigonal planes respectively. We construct an extended Hubbard type model including a deformation potential which is treated in unrestricted Hartree Fock approximation and describes correctly the observed first-order CO transition. We also discuss the influence of associated orbital order. Furthermore we suggest that due to different band fillings AlV$_2$O$_4$ should remain metallic while LiV$_2$O$_4$ under pressure should become a semiconductor when charge disproportionation sets in

Restless legs syndrome and health‐related quality of life in adults with multiple sclerosis

Restless legs syndrome (RLS) is a sleep disorder that may exacerbate many of the symptoms and consequences of multiple sclerosis (MS), and may have further implications for health‐related quality of life (HRQOL). The present study examined the relationships among RLS, symptoms and HRQOL in people with MS. Participants with MS (n = 275) completed the Cambridge‐Hopkins Restless Legs Syndrome Questionnaire, the International Restless Legs Syndrome Study Group Scale, the Multiple Sclerosis Impact Scale, the Pittsburgh Sleep Quality Index, the Fatigue Severity Scale, the Hospital Anxiety and Depression Scale and the Patient Determined Disease Steps. There were 74 (26.9%) persons with MS who had RLS (MS + RLS). The MS + RLS group reported worse physical and psychological HRQOL (p = 0.020 and p = 0.017, respectively) and greater perceived fatigue (p = 0.006) and anxiety symptoms (p = 0.042) than the MS‐only group. Within the MS + RLS group, RLS severity was associated with physical (r = 0.43) and psychological (r = 0.46) HRQOL, sleep quality (r = 0.38), perceived fatigue (r = 0.28), depression (r = 0.38) and anxiety (r = 0.28). The relationships between RLS severity and the domains of HRQOL were attenuated when accounting for fatigue, depression and/or anxiety. Worse RLS severity was associated with reduced HRQOL, which was accounted for by fatigue, depression and anxiety.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155491/1/jsr12880.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155491/2/jsr12880_am.pd

Complex-Orbital Order in Fe_3O_4 and Mechanism of the Verwey Transition

Electronic state and the Verwey transition in magnetite (Fe_3O_4) are studied using a spinless three-band Hubbard model for 3d electrons on the B sites with the Hartree-Fock approximation and the exact diagonalisation method. Complex-orbital, e.g., 1/sqrt(2)[|zx> + i |yz>], ordered (COO) states having noncollinear orbital moments ~ 0.4 mu_B on the B sites are obtained with the cubic lattice structure of the high-temperature phase. The COO state is a novel form of magnetic ordering within the orbital degree of freedom. It arises from the formation of Hund's second rule states of spinless pseudo-d molecular orbitals in the Fe_4 tetrahedral units of the B sites and ferromagnetic alignment of their fictitious orbital moments. A COO state with longer periodicity is obtained with pseudo-orthorhombic Pmca and Pmc2_1 structures for the low-temperature phase. The state spontaneously lowers the crystal symmetry to the monoclinic and explains experimentally observed rhombohedral cell deformation and Jahn-Teller like distortion. From these findings, we consider that at the Verwey transition temperature, the COO state remaining to be short-range order impeded by dynamical lattice distortion in high temperature is developed into that with long-range order coupled with the monoclinic lattice distortion.Comment: 16 pages, 13 figures, 6 tables, accepted for publication in J. Phys. Soc. Jp