Low-dimensional bose liquids: beyond the gross-pitaevskii approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d相似文献   

Annealing effects of phase I poly(vinylidene fluoride)

The effects of annealing temperatures on stretched poly(vinylidene fluoride) film were systematically studied from the “as-received” condition up to the melting range (180°C). X-ray diffraction studies indicate that the annealing process brings about better chain packing and increased crystallite perfection. The elastic modulus and piezoelectric strain and stress constants, d₃, and e₃₁, decrease as the annealing temperature T_a increases up to 160°C, while the remanent polarization P_r remains almost constant. Some of these characteritics may be interpreted in terms of a morphological transformation of microfibrils. The values of P_r, d₃₁, and e₃₁ increase dramatically as T_a increases from 160 to 180°C; P_r increases from 56 to 85 mC/m², d₃₁ from 20.2 to 27.7 pC/N, and e₃₁ from 51.4 to 65.2 mC/m². As a result, the values of P_r and d₃₁ were the largest recorded from any of the samples used in the present study. e₃₁ showed a value close to the largest one; this usually occurs in unannealed samples. Samples annealed in the melting range also exhibit significantly improved ageing characteristics. The large value of P_r and the small relaxation strength of both the dielectric constant and elastic modulus indicates that the largest crystallinity obtained is approximately 70%.     

A continuous function whose divided differences at the Chebyshev extrema are all zero

A nontrivial function having the properties described in the title is given explicitly.     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Giant-cell tumor of the tibia in a child presenting as an expansile metaphyseal lesion with fluid-fluid levels on MR

Approximately two percent of giant-cell tumors (GCT) occur in the skeletally immature. The patient presented is four years old with a cystic giant-cell tumor of the tibial metaphysis. Fluid-fluid levels are demonstrated on CT and MR and likely represent the underlying pathophysiology.     

Associations between Neurocardiovascular Signal Entropy and Physical Frailty

In this cross-sectional study, the relationship between noninvasively measured neurocardiovascular signal entropy and physical frailty was explored in a sample of community-dwelling older adults from The Irish Longitudinal Study on Ageing (TILDA). The hypothesis under investigation was that dysfunction in the neurovascular and cardiovascular systems, as quantified by short-length signal complexity during a lying-to-stand test (active stand), could provide a marker for frailty. Frailty status (i.e., “non-frail”, “pre-frail”, and “frail”) was based on Fried’s criteria (i.e., exhaustion, unexplained weight loss, weakness, slowness, and low physical activity). Approximate entropy (ApEn) and sample entropy (SampEn) were calculated during resting (lying down), active standing, and recovery phases. There was continuously measured blood pressure/heart rate data from 2645 individuals (53.0% female) and frontal lobe tissue oxygenation data from 2225 participants (52.3% female); both samples had a mean (SD) age of 64.3 (7.7) years. Results revealed statistically significant associations between neurocardiovascular signal entropy and frailty status. Entropy differences between non-frail and pre-frail/frail were greater during resting state compared with standing and recovery phases. Compared with ApEn, SampEn seemed to have better discriminating power between non-frail and pre-frail/frail individuals. The quantification of entropy in short length neurocardiovascular signals could provide a clinically useful marker of the multiple physiological dysregulations that underlie physical frailty.     

Application of the dissipation theorem to turbulent flow and mass transfer in a pipe

The dissipation theorem is applied to turbulent pipe flow. The eddy-viscosity profiles can be made to agree with some in the literature in the sense that the eddy viscosity starts at zero on the solid pipe wall, rises to a maximum, and declines again toward the center line. A relationship between the volumetric dissipation and the eddy viscosity is derived by means of an energy balance on a core of fluid of radius r. The question of what exponent to use on the radius in another governing equation is clarified, thereby giving better agreement with experimental data than other values tried. Negative values of the eddy viscosity can be obtained in some regions of the flow field, such as near the center line, and it is suggested that these can be eliminated by slight modification of the decay term. Better agreement with the shapes of friction-factor and mass-transfer curves could be achieved by further (empirical) modification of the stress dependence of parameters in the model.     

An infinite family of convex Brunnian links in $${\mathbb{R}^n}$$

This paper proves that convex Brunnian links exist for every dimension n ≥ 3 by constructing explicit examples. These examples are three-component links which are higher-dimensional generalizations of the Borromean rings.     

Existence of solutions to a new model of biological pattern formation

In this paper we study the existence of classical solutions to a new model of skeletal development in the vertebrate limb. The model incorporates a general term describing adhesion interaction between cells and fibronectin, an extracellular matrix molecule secreted by the cells, as well as two secreted, diffusible regulators of fibronectin production, the positively-acting differentiation factor (“activator”) TGF-β, and a negatively-acting factor (“inhibitor”). Together, these terms constitute a pattern forming system of equations. We analyze the conditions guaranteeing that smooth solutions exist globally in time. We prove that these conditions can be significantly relaxed if we add a diffusion term to the equation describing the evolution of fibronectin.