Singular Pressure Research Articles

MODERN METHODS OF INDENTIFYING THE PREDICTORS OF CARDIO-VASCULAR DISEASES IN CHILDREN AT EARLY STAGES

научный биометрический журнал, который знакомит читателя с клиническими рекомендациями и особенностями применения лекарственных и вакцинных средств у детей, предоставляет исчерпывающую информацию о воздействии лекарственных средств на плод, о проводимых в

On the moving contact line singularity: Asymptotics of a diffuse-interface model

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.

Generation of polygonal gas interfaces by soap film for Richtmyer–Meshkov instability study

A simple method of generating polygonal gas interfaces is proposed by using the soap film technique. Thin pins are used as angular vertexes to connect the adjacent sides of polygonal soap films in order to avoid the pressure singularities around the vertexes caused by the surface tension. As a demonstration, three polygonal interfaces (i.e., square, equilateral triangle and diamond) are created in the test section of a shock tube. Experiments are then carried out for a planar shock wave (Mach number about 1.2) interacting with air/SF6 polygonal interfaces. Numerical simulations are also performed to validate the proposed method of the interface formation. Wave systems and interface structures can be clearly identified in experimental schlieren images and agree well with the numerical results. It is also indicated that the presences of thin pins and fine chamfers only have limited effects on the interface evolution and can be ignored at the very early stage. Experimental and numerical results about the movement of the distorted interface, the width and height of the interface structures are further compared and good agreement is achieved. It is then concluded that the polygonal interface formed by the proposed method is applicable for the Richtmyer–Meshkov instability study.

Self-organized hydrodynamics with congestion and path formation in crowds

A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the density and velocity orientation. Short-range repulsion is included through a singular pressure which becomes infinite at the jamming density. The singular limit of infinite pressure stiffness leads to phase transitions from compressible to incompressible dynamics. The paper proposes an Asymptotic-Preserving scheme which takes care of the singular pressure while preventing the breakdown of the Courant–Friedrichs–Lewy (CFL) stability condition near congestion. It relies on a relaxation approximation of the system and an elliptic formulation of the pressure equation. Numerical simulations of impinging clusters show the efficiency of the scheme to treat congestions. A two-fluid variant of the model provides a model of path formation in crowds.

Interaction of rocking vibration of a buried rigid circular disc and a two-layer transversely isotropic half-space

A linear elastic layer of finite thickness bonded on a half-space each containing a transversely isotropic material is considered. A rigid circular disc attached to the interface of these two domains is considered to be affected by a rocking vibration of constant amplitude. With the aid of a scalar potential function, the equations of motion in each domain are solved using Fourier series and Hankel integral transforms. Because of the involved integral transforms, the mixed boundary value problem is changed to dual integral equations; which are reduced to Fredholm integral equations. Because of the complex integrand function existing in the dynamic case, analytical solution cannot be given in general. However, a closed-form solution is introduced for the static case, which itself degenerates to the solution for an isotropic case existing in the literature. The contact stress in between the rigid disc and the surrounding media, and the related impedance function are analytically determined in the static case. With the help of contour integration, the governing Fredholm integral equations are numerically evaluated in the dynamic case. The dynamic contact pressure and the impedance function are numerically evaluated in a general dynamic case. The shape induced singularity in the contact pressure is investigated in detail. Some numerical evaluations are given for different transversely isotropic materials to show the effect of anisotropy.

Coupling schemes for modeling hydraulic fracture propagation using the XFEM

We describe coupled algorithms that use the Extended Finite Element Method (XFEM) to solve the elastic crack component of the elasto-hydrodynamic equations that govern the propagation of hydraulic fractures in an elastic medium. With appropriate enrichment, the XFEM resolves the Neumann to Dirichlet (ND) map for crack problems with O(h2) accuracy and the Dirichlet to Neumann (DN) map with O(h) accuracy. For hydraulic fracture problems with a lag separating the fluid front from the fracture front, we demonstrate that the finite pressure field makes it possible to use a scheme based on the O(h2) XFEM solution to the ND map. To treat problems in which there is a coalescence of the fluid and fracture fronts, resulting in singular tip pressures, we developed a novel mixed algorithm that combines the tip width asymptotic solution with the O(h2) XFEM solution of the ND map away from the tips. Enrichment basis functions required for these singular pressure fields correspond to width power law indices λ>12, which are different from the index λ=12 of linear elastic fracture mechanics. The solutions obtained from the new coupled XFEM schemes agree extremely well with those of published reference solutions.

Narrow resonances and black-hole-like absorption in a non-black-hole metric

A massive body with the Schwarzschild interior metric (perfect fluid of constant density) develops a pressure singularity at the origin when the radius of the body $R$ approaches $9{r}_{s}/8$, where ${r}_{s}$ is the Schwarzschild radius. We show that a quantum scalar particle scattered in this gravitational field possesses a dense spectrum of narrow resonances. Their density and lifetimes tend to infinity in the limit $R\ensuremath{\rightarrow}9{r}_{s}/8$, and we determine the cross section of the particle capture into these quasibound states. Therefore, a body that is not a black hole demonstrates black-hole-like absorption.

Bianchi-I spacetimes in loop quantum cosmology: physics of singularity resolution

Quantum geometry effects in loop quantum cosmology are known to resolve various singularities in the isotropic and anisotropic models. Previous investigations have shown that singularity resolution is tied to boundedness of physical quantities such as the energy density and the expansion and shear scalars in the spacetime. Using effective dynamics, we show that these do not necessarily lead to a generic boundedness of spacetime curvature in the Bianchi-I model and find the potential possibilities where the curvature invariants can diverge. These include cases where the pressure of the matter content diverges at a finite volume and energy density. By analyzing the strength of singularities, we show that such pressure singularities are weak. All known types of strong singularities of the classical theory are resolved. This analysis brings us closer to generalize the results on generic resolution of singularities in the isotropic models in loop quantum cosmology, to the anisotropic spacetimes.

Cosmological tests of sudden future singularities

We discuss combined constraints, coming from the cosmic microwave background shift parameter $\mathcal{R}$, baryon acoustic oscillations (BAO) distance parameter $\mathcal{A}$, and from the latest type Ia supernovae data, imposed on cosmological models which allow sudden future singularities of pressure. We show that due to their weakness such sudden singularities may happen in the very near future and that at present they can mimic standard dark energy models.

Numerical simulations of the Euler system with congestion constraint

In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in [6,17] with the constraint introduced into the system by a singular pressure law, which causes the transition of different asymptotic dynamics between different regions. To overcome these difficulties, we adapt and implement two asymptotic preserving (AP) schemes originally designed for low Mach number limit [16,18] to our model. These schemes work for the different dynamics and capture the transitions well. Several numerical tests both in one dimensional and two dimensional cases are carried out for our schemes.

Two-phase pressure drop in return bends: Experimental results for R-410A

This study presents 238 pressure drop data points measured for two-phase flow of R-410A in horizontal return bends. The tube diameter ( D) varies from 7.90 to 10.85 mm and the curvature ratio (2 R/ D) from 3.68 to 4.05. The mass velocity ranges from 179 to 1695 kg m −2 s −1 and the saturation temperatures from 4.6 °C to 20.7 °C. Preliminary tests show that the recovery length necessary for a correct pressure drop measurement downstream of the return bend is less than 20 D, for the experimental conditions covered in this study. The singular pressure drop is determined by subtracting the regular pressure drop in straight tube from the total pressure drop. The experimental data are compared against four available correlations found in the literature. The present experimental database for the return bend pressure drop is presented in the Appendix A.

Analysis on the Contact Pressure Distribution of Chemical Mechanical Polishing by the Bionic Polishing Pad with Phyllotactic Pattern

In order to make the contact pressure distribution of polishing wafer surface more uniform during chemical mechanical polishing (CMP), a kind of the bionic polishing pad with sunflower seed pattern has been designed based on phyllotaxis theory, and the contact model and boundary condition of CMP have been established. Using finite element analysis, the contact pressure distributions between the polishing pad and wafer have been obtained when polishing silicon wafer and the effects of the phyllotactic parameter of polishing pad on the contact pressure distribution are found. The results show that the uniformity of the contact pressure distribution can be improved and the singularity of the contact pressure in the boundary edge of polished wafer can be decreased when the reasonable phyllotactic parameters are selected.

Viscous flows in corner regions: Singularities and hidden eigensolutions

AbstractNumerical issues arising in computations of viscous flows in corners formed by a liquid–fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the ‘moving contact‐line problem’ and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite‐element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh‐dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh‐independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite‐element method in the context of the present problem are discussed. Copyright © 2009 John Wiley & Sons, Ltd.

The fallacy of Oppenheimer Snyder collapse: no general relativistic collapse at all, no black hole, no physical singularity

By applying Birkhoff’s theorem to the problem of the general relativistic collapse of a uniform density dust, we directly show that the density of the dust ρ=0 even when its proper number density n would be assumed to be finite! The physical reason behind this exact result can be traced back to the observation of Arnowitt et al. (Phys. Rev. Lett. 4: 375, 1960) that the gravitational mass of a neutral point particle is zero: m=0. And since, a dust is a mere collection of neutral point particles, unlike a continuous hydrodynamic fluid, its density ρ=mn=0. It is nonetheless found that for k=−1, a homogeneous dust can collapse and expand special relativistically in the fashion of a Milne universe. Thus, in reality, general relativistic homogeneous dust collapse does not lead to the formation of any black hole in conformity of many previous studies (Logunov et al., Phys. Part. Nucl. 37: 317, 2006; Kiselev et al., Theor. Math. Phys. 164: 972, 2010; Mitra, J. Math. Phys. 50: 042502, 2009a; Suggett, J. Phys. A 12: 375 1979b). Interestingly, this result is in agreement with the intuition of Oppenheimer and Snyder (Phys. Rev. 56: 456, 1939) too:“Physically such a singularity would mean that the expressions used for the energy-momentum tensor does not take into account some essential physical fact which would really smooth the singularity out. Further, a star in its early stages of development would not possess a singular density or pressure, it is impossible for a singularity to develop in a finite time.”

On the pressure and stress singularities induced by steady flows of a pair of nonmiscible, incompressible, viscous fluids in contact with a wall

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, only of late has there been much in the way of corresponding identifications of flow-induced stress singularities in fluid mechanics. These recent asymptotic identifications are for a single incompressible viscous fluid: Here the asymptotic approach is extended to apply to a configuration entailing two such fluids. For this configuration, various specifications leading to power or log singularities are determined. These results demonstrate that flow-induced stress singularities can occur in a structural container at a location where no singularities are identified within solid mechanics alone.

Dark energy from temporal and spatial singularities of pressure

AbstractI describe an opportunity to mimic dark energy leading to a current acceleration of the universe by the application of the pressure singularities surrounding an observer. Two essentially different models are investigated. In the first one, the acceleration is due to an approach to a pressure singularity which appears on a constant time hypersurface. In the second one, the acceleration is due to the existence of the pressure singularities in some regions of space. Both models are tested positively against observations.

Dark energy from temporal and spatial singularities of pressure

Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.Received 15 November 2009, accepted 4 January 2010Published online XXXKey words exotic singularities, inhomogeneous models, dark energyPACS 04.20.Dw; 11.25.-w; 98.80.Es; 98.80.JkI describe an opportunity to mimic dark energy leading to a current acceleration of the universe by theapplication of the pressure singularities surrounding an observer. Two essentially different models are in-vestigated. In the first one, the acceleration is due to an approach to a pressure singularity which appearson a constant time hypersurface. In the second one, the acceleration is due to the existence of the pressuresingularities in some regions of space. Both models are tested positively against observations.

Discussion on the stability of heated channels with different fluids at supercritical pressures

The paper extends previous work on the stability of heated channels with fluids at supercritical pressure as predicted by available models. A set of dimensionless numbers proposed to predict the threshold of instabilities is further discussed to highlight their capabilities and possible improvements. In particular, it is shown that the choice made for the reference value of the derivative of specific volume with respect to specific enthalpy is justified as an extension of classical formulations adopted for boiling channels. Moreover, the degree of universality to be expected by the use of these dimensionless numbers while using different fluids is clarified; in this aim four different fluids are considered: water, carbon dioxide, ammonia and refrigerant R23. In order to provide a clear perspective of the usefulness of the proposed dimensionless numbers for dealing with different fluids, linear stability maps generated by a previously developed in-house code, making use of balance equations in dimensionless form, are then compared with the results obtained by computations performed in dimensional terms. In this aim, both an in-house code and RELAP5 are used. The reference considered system is a long circular channel with uniform heating and no singular pressure drops, already addressed in previous analyses, here assumed both in vertical upward and in horizontal flow conditions. The comparison of the predictions obtained for the different fluids allows to ascertain the level of applicability of the dimensionless numbers and, as an interesting by-product, confirms the possibility to encounter static instabilities also in systems at supercritical pressure.

Free boundary value problem for a viscous two-phase model with mass-dependent viscosity

In this paper, we study a free boundary value problem for two-phase liquid–gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum with a discontinuity. This is an extension of the paper [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid–gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV]. Just as in [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid–gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV], the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions when β ∈ ( 0 , 1 ] , which have improved the previous result of Evje and Karlsen, and get the asymptotic behavior result, also we obtain the regularity of the solutions by energy method.

On the pressure and stress singularities induced by steady flows of incompressible viscous fluids

Design for structural integrity requires an appreciation of where stress singularities can occur in structural configurations. While there is a rich literature devoted to the identification of such singular behavior in solid mechanics, to date there has been relatively little explicit identification of stress singularities caused by fluid flows. In this study, stress and pressure singularities induced by steady flows of viscous incompressible fluids are asymptotically identified. This is done by taking advantage of an earlier result that the Navier–Stokes equations are locally governed by Stokes flow in angular corners. Findings for power singularities are confirmed by developing and using an analogy with solid mechanics. This analogy also facilitates the identification of flow-induced log singularities. Both types of singularity are further confirmed for two global configurations by applying convergence–divergence checks to numerical results. Even though these flow-induced stress singularities are analogous to singularities in solid mechanics, they nonetheless render a number of structural configurations singular that were not previously appreciated as such from identifications within solid mechanics alone.