Well-behaved Solutions Research Articles

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.

Robust Simulation of a TaO Memristor Model

This work presents a continuous and differen- tiable approximation of a Tantalum oxide memristor model which is suited for robust numerical simulations in soft- ware. The original model was recently developed at Hewlett Packard labs on the basis of experiments carried out on a memristor manufactured in house. The Hewlett Packard model of the nano-scale device is accurate and may be taken as reference for a deep investigation of the capabilities of the memristor based on Tantalum oxide. However, the model contains discontinuous and piecewise differentiable func- tions respectively in state equation and Ohm's based law. Numerical integration of the differential algebraic equation set may be significantly facilitated under substitution of these functions with appropriate continuous and differentiable ap- proximations. A detailed investigation of classes of possible continuous and differentiable kernels for the approximation of the discontinuous and piecewise differentiable functions in the original model led to the choice of near optimal can- didates. The resulting continuous and differentiable DAE set captures accurately the dynamics of the original model, delivers well-behaved numerical solutions in software, and may be integrated into a commercially-available circuit sim- ulator.

Birth Rate Effects on an Age-Structured Predator-Prey Model with Cannibalism in the Prey

We develop a family of predator-prey models with age structure and cannibalism in the prey population. It consists of systems ofmordinary differential equations, wheremis a parameter associated with new proposed prey birth rates. We discuss how these new birth rates give the required flexibility to produce differential systems with well-behaved solutions. The main feature required in these models is the coexistence among the involved species, which translates mathematically into stable equilibria and periodic solutions. The search for such characteristics is based on heuristic predation functions that account for cannibalism in the prey.

An example where lubrication theory comes short: hydraulic jumps in a flow down an inclined plate

AbstractWe examine two-dimensional flows of a viscous liquid on an inclined plate. If the upstream depth $h_{-}$ of the liquid is larger than its downstream depth $h_{+}$, a smooth hydraulic jump (bore) forms and starts propagating down the slope. If the inclination angle of the plate is small, the bore can be described by the so-called lubrication theory. In this work we demonstrate that bores with $h_{+}/h_{-}<(\sqrt{3}-1)/2$ either are unstable or do not exist as steady solutions of the governing equation (physically, these two possibilities are difficult to distinguish). The instability/evolution occurs near a stagnation point and, generally, causes overturning – sometimes on the scale of the whole bore, sometimes on a shorter, local scale. The overturning occurs because the flow advects disturbances towards the stagnation point and, thus, ‘compresses’ them, increasing the slope of the free surface. Interestingly, this effect is not captured by the lubrication theory, which formally yields a well-behaved stable solution for all values of $h_{+}/h_{-}$.

Near-BPS Skyrmions: Constant baryon density

Although it provides a relatively good picture of the nucleons, the Skyrme Model is unable to reproduce the small binding energy in nuclei. This suggests that Skyrme-like models that nearly saturate the Bogomol'nyi bound may be more appropriate since their mass is roughly proportional to the baryon number A. For that purpose, we propose a near-BPS Skyrme Model. It consists of terms up to order six in derivatives of the pion fields, including the nonlinear and Skyrme terms which are assumed to be relatively small. For our special choice of mass term, we obtain well-behaved analytical BPS-type solutions with constant baryon density configurations, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme Model. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon B/A with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.

On balanced moving mesh methods

Moving mesh methods are a widely used approach in the numerical solution of PDEs where the original PDEs are transformed from a physical domain to a computational domain. The objective is to utilize a uniform mesh in the computational domain to get a non-uniform physical mesh that better captures the behavior of the solution. The movement of the physical mesh points can be governed by a moving mesh PDE associated with a corresponding monitor function and both the original PDEs and the moving mesh PDEs must be solved simultaneously. The motivation for this paper is to study a balanced moving mesh method, where the aim is to strike a balance between the properties of the solution of the original PDE and that of the moving mesh PDE. We focus on particular choices of the monitor function that give both a well-behaved mesh transformation and a well-behaved solution in the computational domain. Both theoretical analysis and numerical experiments are presented as illustrations.

Subharmonic functions in sub-Riemannian settings

In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution \Gamma . These characterizations are based on suitable average operators on the level sets of \Gamma . Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks. We analyze as well the notion of subharmonic function in the weak sense of distributions, and we show how to approximate subharmonic functions by smooth ones. The classes of operators involved are wide enough to comprise, as very special cases, the sub-Laplacians on Carnot groups. The results presented here generalize and carry forward former results of the authors in [6, 8].

Dynamic Finite Size Effects in Spiking Neural Networks

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter.

Logic-based topological representation of vague moving regions: computational models for well-behaved GIS solutions

This study proposes a solution for the topological representation and interpretation of moving regions under vagueness in a geographic information system (GIS). The problem is multifaceted, and different aspects will be discussed. We investigate the impact of several types of fuzzy logic on results and address which is more convenient for the region connection calculus under fuzziness (FRCC). By recognising that the main and basic relation to evaluate topological relations is the connection relation, we adopt a qualitative strategy based on fuzzy inference and resemblance relations. We also define topological differences and introduce fuzzy transition relations (FTRs) to distinguish how a transition from one topological situation to another occurs for a pair of objects during a time period. As pure topological relations are not sufficient for a complete qualitative perception, an orientation-based method (OBM) will be proposed. Using this method, we can interpret, for example, a region that partially overlaps another region mostly on its northern part. Most importantly, some step-by-step algorithms and constructs are proposed and evaluated such that the model can apply to regions stored in vector data models.

The Dirichlet problem and the inverse mean‐value theorem for a class of divergence form operators

The aim of this paper is to study some classes of second-order divergence-form partial differential operators ℒ of sub-Riemannian type. Our main assumption is the C∞-hypoellipticity of ℒ, together with the existence of a well-behaved fundamental solution Γ(x, y) for ℒ. We consider the mean-integral operator Mr naturally associated to the mean-value theorem for the ℒ-harmonic functions and we investigate the following topics: the positivity set of the kernel associated to Mr; the role of Mr in solving the homogeneous Dirichlet problem related to ℒ in the Perron–Wiener–Brelot sense; the existence of an inverse mean-value theorem characterizing the sub-Riemannian ‘balls’ Ωr(x), superlevel sets of Γ(x,·). This last result extends a previous theorem by Kuran [Bull. London Math. Soc. 1972]. As side-results, we provide a short proof of the Strong Maximum Principle for ℒ using Mr, a Poisson–Jensen formula for the ℒ-subharmonic functions and several results concerning the geometry of the sets Ωr(x).

Relativistic modelling of a superdense star containing a charged perfect fluid

The paper presents a variety of classes of interior solutions of the Einstein-Maxwell field equations for a static, spherically symmetric distribution of a charged fluid of well-behaved nature. They describe perfect fluid balls with positive finite central pressure and density; their ratio is less than one (c = 1), and the causality condition is obeyed at the center. The outmarch of pressure, density, pressuredensity ratio and the adiabatic speed of sound is a monotonic decrease, in a physically appealing manner. A certain class of these well-behaved solutions is studied extensively. For this class, the mass of the configuration is maximized. In particular, for a surface density ρb = 2×1014 g/cm3 we obtain a star with a maximummass of 3.47M⊙, a radius of 15.21 km and the central redshift 1.014385.

Continuous penalty forces

We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm computes a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace contact features along their deforming trajectories and accumulate penalty forces along the penetration time intervals between the overlapping feature pairs. Moreover, we present a closed-form expression to compute the continuous and smooth collision response. Our method has very small additional overhead compared to previous penalty methods, and can significantly improve the stability and robustness. We highlight its benefits on several benchmarks.

Near-BPS Skyrmions: Nonshell configurations and Coulomb effects

The relatively small binding energy in nuclei suggests that they may be well represented by near-BPS Skyrmions since their mass is roughly proportional to the baryon number $A.$ For that purpose, we propose a generalization of the Skyrme model with terms up to order six in derivatives of the pion fields and treat the nonlinear $\sigma$ and Skyrme terms as small perturbations. For our special choice of mass term (or potential) $V$, we obtain well-behaved analytical BPS-type solutions with non-shell configurations for the baryon density, as opposed to the more complex shell-like configurations found in most extensions of the Skyrme model . Along with static and (iso)rotational energies, we add to the mass of the nuclei the often neglected Coulomb energy and isospin breaking term. Fitting the four model parameters, we find a remarkable agreement for the binding energy per nucleon $B/A$ with respect to experimental data. These results support the idea that nuclei could be near-BPS Skyrmions.

Subsolidus formation and impedance spectroscopy studies of materials in the (Bi2O3)1−x (Y2O3)x binary system

Single phase (Bi2O3)1−x(Y2O3)x samples with x=0.15, 0.20, 0.30 and 0.40 were successfully synthesised via conventional solid state method at the firing temperature of 800°C over 24h. These samples crystallised in cubic fluorite structure, space group, Fm-3m and lattice parameters, a ranging from 5.5167Å to 5.4369Å with an increase of doped Y2O3. The linear-plot obeyed Vegard's law, revealing a well-behaved substitutional solid solution existed within the incorporated dopant concentration range. (Bi2O3)1−x(Y2O3)x subsolidus system was thermally stable as no phase transition or weight loss was discernable within the studied temperature. The electrical properties of the prepared samples were characterised by AC impedance analyser, HP4192 at temperature ranging from 25°C to 850°C in the frequency range of 5Hz to 13MHz. The impedance data could be represented by different RC equivalent circuits. The conduction mechanism involved two processes with different activation energies at low and high temperature regions, e.g. 1.09–1.12eV and 0.41–0.44eV, respectively. The ionic conductivities of the prepared samples were found decreased with increase of yttrium content. These values were in general higher than that of commercial yttria- stabilised zirconia (YSZ) solid electrolyte over wide range of temperatures.

Existence of singularities in two-Kerr black holes

We show that the angular momentum—area inequality 8π|J| ⩽ A for weakly stable minimal surfaces would apply to I+-regular many-Kerr solutions, if any existed. Hence, we remove the undesirable hypothesis in the Hennig–Neugebauer proof of non-existence of well-behaved two-component solutions.

Information-based distance measures and the canonical reflection of view updates

For the problem of reflecting an update on a database view to the main schema, the constant-complement strategies are precisely those which avoid all update anomalies, and so define the gold standard for well-behaved solutions to the problem. However, the families of view updates which are supported under such strategies are limited, so it is sometimes necessary to go beyond them, albeit in a systematic fashion. In this work, an investigation of such extended strategies is initiated for relational schemata. The approach is to characterize the information content of a database instance, and then require that the optimal reflection of a view update to the main schema embody the least possible change of information. The key property is identified to be strong monotonicity of the view, meaning that view insertions may always be reflected as insertions to the main schema, and likewise for deletions. In that context it is shown that for insertions and deletions, an optimal update, entailing the least change of information, exists and is unique up to isomorphism for wide classes of constraints.

Passing Through the Wind Turbine Thrust Singularity

I T HAS long been known that the popular and useful controlvolume actuator-disk model for wind turbines encounters a troublesome behavior as the thrust coefficient for the rotor/disk approaches 1, which occurs when the velocity at the rotor/disk approaches half that of the freestream level and the axial velocity at the downstream outlet approaches zero. This is discussed in detail in nearly all texts and papers involving wind turbines (as, for example, in [1–8]). Beyond a thrust-coefficient value of 1, it is well understood that the current version of the model does not apply, because it predicts flow entering the control volume at the downstream outlet, thus negating its further use and leaving a gap in the theory for an important range of the controlling parameters. To date, this gap has been addressed largely with either empirical expressions and/or computational fluid dynamics (CFD) methods. Based on Glauert’s 1926 analysis of data taken for windmilling helicopter blades in open-jet wind tunnels (as discussed in [1]) and its adaption to wind turbines by Stoddard [5], it is now widely accepted that the classical model begins to break down somewhere near a rotor/disk velocity ratio of 0.6 (induction factor of 0.4). For larger induction factors, it is assumed that a turbulent-wake state ensues, with reverse and/or unsteady flow effects dominating the flow as the rotor/disk velocity further reduces to zero: i.e., the rotor/disk stalls. It is further widely accepted that Glauert’s empirical expression for the rotor/disk performance prevails in this turbulent-wake region, with several attempts at improving its utility, as summarized by Buhl [8]. Additionally, recent CFD studies by Sorensen et al. [6] andMikkelsen [7] appear to reinforce this empirical model. Recently, however, two studies [9,10] using control-volume actuator-disk modeling of wind-tunnel blockage influences on rotor/ disk performance uncovered an entirely new family of well-behaved steady-state solutions that exist in the turbulent-wake parameter space: i.e., for induction factors from 0.4 all the way to 1. Moreover, the results of [9] implied the existence of a new well-behaved solution family for induction factors above 0.5, even for the zeroblockage condition. The current work provides this new exact solution for induction factors from 0.5 to 1 based on a limit-analysis solution of the control-volume actuator-disk equations. This new solution provides the heretofore missing piece of the basic theory, filling the gap for induction factors of 0.5 to 1. Comparisons of the new analytical solutions with experiments and CFD studies of actuator disks provide strong evidence of its validity. The relevance of the results to CFD modeling, wind-tunnel testing, and/or field testing of wind turbines is discussed.

Modification of encapsulation pressure of reverse micelles in liquid ethane

Encapsulation within reverse micelles dissolved in low viscosity fluids offers a potential solution to the slow tumbling problem presented by large soluble macromolecules to solution NMR spectroscopy. The reduction in effective macromolecular tumbling is directly dependent upon the viscosity of the solvent. Liquid ethane is of sufficiently low viscosity at pressures below 5000 psi to offer a significant advantage. Unfortunately, the viscosity of liquid ethane shows appreciable pressure dependence. Reverse micelle encapsulation in liquid ethane often requires significantly higher pressures, which obviates the potential advantages offered by liquid ethane over liquid propane. Addition of co-surfactants or co-solvents can be used to manipulate the minimum pressure required to obtain stable, well-behaved solutions of reverse micelles prepared in liquid ethane. A library of potential additives is examined and several candidates suitable for use with encapsulated proteins are described.

Subharmonic functions in sub-Riemannian settings

In this note we present mean value characterizations of subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution i. These characterizations are based on suitable average operators on the level sets of i. Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Rado, Beckenbach and Reade. The results presented here generalize and carry forward former results of the authors in [6, 8].

Noncommutative double scalar fields in FRW cosmology as cosmical oscillators

We investigate the effects caused by noncommutativity of the phase space generated by two scalar fields that have non-minimal conformal couplings to the background curvature in the FRW cosmology. We restrict deformation of the minisuperspace to noncommutativity between the scalar fields and between their canonical conjugate momenta. Then, the investigation is carried out by means of a comparative analysis of the mathematical properties (supplemented with some diagrams) of the time evolution of variables in a classical model and the wavefunction of the universe in a quantum perspective, both in the commutative and noncommutative frames. We find that the imposition of noncommutativity causes more ability in tuning time solutions of the scalar fields and, hence, has important implications in the evolution of the Universe. We find that the noncommutative parameter in the momenta sector is the only responsible parameter for the noncommutative effects in the spatially flat universes. A distinguishing feature of the noncommutative solutions of the scalar fields is that they can be simulated with the well-known three harmonic oscillators depending on three values of the spatial curvature, namely the free, forced and damped harmonic oscillators corresponding to the flat, closed and open universes, respectively. In this respect, we call them cosmical oscillators. In particular, in closed universes, when the noncommutative parameters are small, the cosmical oscillators have an analogous effect with the familiar beating effect in the sound phenomena. Some of the special solutions in the classical model and the allowed wavefunctions in the quantum model make bounds on the values of the noncommutative parameters. The existence of a non-zero constant potential (i.e. a cosmological constant) does not change time evolutions of the scalar fields, but modifies the scale factor. An interesting feature of the well-behaved solutions of the wavefunctions is that the functional form of the radial part is the same as the commutative ones within a given replacement of constants caused by the noncommutative parameters. Furthermore, the Noether theorem has been employed to explore the effects of noncommutativity on the underlying symmetries in the commutative frame. Two of the six Noether symmetries of spatially flat universes, in general, are retained in the noncommutative case, and one out of the three in non-flat universes.