Order Terms Research Articles

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation which quantifies the mesh resolution of the geometry of the interface. Numerical examples are presented to illustrate the competitive performance of the method.

Traditional Institutions and Good Governance in Nigeria

Traditional institutions as custodian of cultures and traditions have continued to play a very significant role before and during colonial independence of many African societies. In Nigeria they provide a system of administration with an utmost aim of maintaining a stable governance through tradition, customs, and law and order. But with the advent of democracy, the role of traditional institutions became less recognized in the democratic system of government. The paper examined the role and relevance of indigenous traditional institutions to good governance. The paper was a quantitative research. Data was obtained from secondary sources including journals, articles and publications. The paper revealed that traditional institutions play a very significant role of sustaining culture and traditions, informally managing of conflict, maintaining peace, custodian of oral traditional history of the people etc. before and during colonial era. But with the advent of democracy, their power and duties became less recognized in the democratic system of government because traditional institutions were negated to the back door and politicized. Functionalism theory of Emile Durkheim (1858 – 1917) was employed to explain how society is an integrated whole, where all parts are interconnected and traditional institutions as part of the society, play a vital function of maintaining stability and contributing to the wellbeing of its members in terms of law, order and governance. The paper concluded that if the goal of government at all levels is to provide good governance to the people, rapid in social wealth and economic development, traditional institutions need to be integrated and assigned greater responsibilities in Nigerian’s contemporary democratic system of government because they have the ability to promote grassroots governance and facilitate access of rural communities to public services.

The long-time asymptotics of the derivative nonlinear Schr[formula omitted]dinger equation with step-like initial value

Consideration in this present paper is the long-time asymptotics of solutions to the derivative nonlinear Schrödinger (DNLS) equation with the step-like initial value q(x,0)=q0(x)=A1eiϕe2iBx,x<0,A2e−2iBx,x>0,by Deift–Zhou method. The step-like initial problem is described by a matrix Riemann–Hilbert problem. A crucial ingredient used in this paper is to introduce the g-function mechanism for solving the problem of the entries of the jump matrix growing exponentially as t→∞. It is shown that the leading order term of the long-time asymptotics solution of the DNLS equation is expressed by the Theta function Θ about the Riemann-surface of genus 3 and the subleading order term expressed by parabolic cylinder and Airy functions.

Optimal Decision for Repairable Products Sale and Warranty under Two-Dimensional Deterioration with Consideration of Production Capacity and Customers’ Heterogeneity

An effective warranty policy is not only an obligation for the manufacturer or vendor, but it also enhances the willingness of customers to purchase from them in the future. To earn more customers and increase sales, manufacturers or vendors should be inclined to prolong the service life of their products as an effort to gain more customers. Nevertheless, manufacturers or vendors will not provide a boundless warranty in order to dominate the market, since the related warranty costs will eventually exceed the profits in the end. Therefore, it is a question of weighing the advantage of extending the warranty term in order to earn the trust of new customers against the investment. In addition, since deterioration depends on both time and usage, the deterioration estimation for durable products may be incorrect when considering only one factor. For such problems, a two-dimensional deterioration model is suitable, and the failure times are drawn from a non-homogeneous Poisson process (NHPP). Moreover, customers’ heterogeneity, manufacturers’ production capacity, and preventive maintenance services are also considered in this study. A mathematical model with the corresponding solution algorithm is proposed to assist manufacturers in making systematic decisions about pricing, production, and warranty. Finally, managerial implications are also provided for refining related decision-making.

Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors

In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are C∞. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented.

Long-time behaviour of solutions of superlinear systems of differential equations

ABSTRACT This paper establishes the precise asymptotic behaviour, as time t tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the spatial variables are small, is not linear, but rather positively homogeneous of a degree greater than one. We prove that the solution behaves like , as , for a nonzero vector ξ and an explicit number p>0.

Dislocation-mediated brittle-ductile transition of diamond under high pressure

Recent confirmation of room temperature dislocation plasticity in single-crystal diamond and the activation of {001}<110> slip system in experiments has opened up a new era to understand the deformation mechanism of brittle covalent crystals. However, few theoretical research and simulation has been conducted on the dislocation gliding in {001}<110> slip system. In this work, a new potential function is derived from the original Tersoff potential to the Tersoff High Pressure potential with a novel bond order term with the nearest neighbors. This model has been validated with series of molecular dynamic simulations of both {001}<110> and {111}<110> dislocation slip systems in diamond, successfully describing the dislocation mediated brittle-ductile transition under high hydrostatic pressure. The gliding mechanism of dislocation on {001} plane presents a jumping character with a large burgers vector under high hydrostatic pressure. Whereas, the diamond exhibits a zipper-like Griffith cleavage upon shearing under zero hydrostatic pressure. Similar deformation processes are also found in polycrystalline diamond. The current model is expected to prove useful in related simulations focusing on the strengthening mechanism in diamond and related research.

A two-stage Polynomial Chaos Expansion application for bound estimation of uncertain FRFs

Polynomial Chaos Expansion (PCE) is a method for analysing uncertain vibratory structures with lower computational effort. It may simply be described as a curve fitting method with orthogonal basis terms, where the polynomial type, dimension and order are predefined for the uncertain responses. However, the polynomial order in PCE must be very high to accurately estimate statistical moments of the frequency response function in resonance regions of lightly damped and uncertain structures. To solve this issue different transformation techniques are reported in the literature, where implementations of PCE produce higher accuracy with a lower order polynomial. However, these transformations lose the attraction for using PCE, since they require some additional mathematical operations and, mostly, they present high accuracy if the higher orders of polynomials are again of interest. In this study, an efficient approach is presented for the upper bound estimation of the uncertain frequency response functions (FRFs) via PCE with lower order terms without performing any transformation. Rather than one-stage application of PCE for the desired response of an uncertain problem, the approach comprises a two-stage application of the classical PCE, i.e. first for the natural frequencies and then for the FRF calculations. As an example application of the approach, a thin beam for two different uncertainty cases is considered, namely local and global uncertainty. The local and global input uncertainties are generated by variability of lumped masses added at the boundary and Young's modulus, respectively. The FRF bounds are compared with extensive experimental and numerical Monte Carlo simulations, showing that low order polynomials are sufficient to calculate the bounds accurately with the technique described.

Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term

Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term

Black holes in R2-dRGT massive gravity

Massive gravity offers an interesting modification of general relativity by considering a nonzero mass for the graviton. We present a de Rham, Gabadadze and Tolley (dRGT) massive gravity model in the presence of higher order curvature gravity. We obtain a spherical solution for the field equations in this theory. The spherical solution possesses an electric charge and a cosmological constant, and it reduces to the Schwarzschild solution in the limit of a negligible graviton mass and the absence of the higher order term. We study the thermodynamics of this black hole and find that the mass of the graviton and the higher order term of gravity have a significant effect on the thermodynamic properties of the black hole. We also show the entropy of a black hole is independent of the mass of the graviton. Using the observational constraints on the coefficient of the higher order term, we determine an upper limit for the graviton mass. We compute the other thermodynamic quantities, such as heat capacity and Helmholtz free energy. Assuming that the spherical solutions are the modified Schwarzschild, we consider the relativistic thin accretion disk and study the effects of higher order term on thermal properties of the disk at the infrared limit in an asymptotic safety scenario.

What is reciprocity? A review and expert-based classification of cooperative transfers

After decades of research on the topic of reciprocity, there is still no consensus about the meaning of the term. Instead, there has been a proliferation of reciprocity terms with varied definitions, some of which overlap in ways that lead to confusion for scholars studying cooperation. In this paper, we provide a summary of 34 reciprocity terms and their definitions from across a variety of disciplines. We then report the results of a survey of cooperation experts spanning biology, anthropology, economics, sociology, and psychology (N = 85) about the extent to which they consider 30 of these definitions of reciprocity to be truly reciprocity. Experts also rated the extent to which they considered seventeen hypothetical scenarios to be examples of reciprocity. We used exploratory factor analysis and found that responses clustered around four dimensions of transfers: Balanced (e.g., Balanced reciprocity), Reputation-based (e.g., Generalized reciprocity), Debt-based (e.g., Calculated reciprocity), and Unconditional (e.g., Negative reciprocity). Although researchers agreed that the term reciprocity was useful and necessary, there was low agreement among scholars about what should be considered reciprocity. However, there was high agreement that unconditional transfers, which are characterized by a lack of expectations of repayment, should not be considered reciprocity. We propose that scholars of cooperation consider using these four dimensions when referring to cooperative transfers rather than using reciprocity terms in order to facilitate communication across disciplines, resolve issues related to ambiguous definitions of reciprocity, and provide a solution to the lack of consensus about what constitutes reciprocity.

Liouville results for fully nonlinear equations modeled on Hörmander vector fields: II. Carnot groups and Grushin geometries

This paper treats second order fully nonlinear degenerate elliptic equations having a family of subunit vector fields satisfying a full-rank bracket condition. It studies Liouville properties for viscosity sub- and supersolutions in the whole space, namely, under a suitable bound at infinity from above and, respectively, from below, they must be constants. In a previous paper, we proved an abstract result and discussed operators on the Heisenberg group. Here, we consider various families of vector fields: the generators of a Carnot group, with more precise results for those of step 2, in particular H-type groups and free Carnot groups, the Grushin and the Heisenberg-Greiner vector fields. All these cases are relevant in sub-Riemannian geometry and have in common the existence of a homogeneous norm that we use for building Lyapunov-like functions for each operator. We give explicit sufficient conditions on the size and sign of the first and 0-th order terms in the equations and discuss their optimality. We also outline some applications of such results to the problem of ergodicity of multidimensional degenerate diffusion processes in the whole space.

Unexpected biases between congruence classes for parts in k-indivisible partitions

For integers k,t≥2, and 1≤r≤t let Dk×(r,t;n) be the number of parts among all k-indivisible partitions of n (i.e., partitions where all parts are not divisible by k) of n that are congruent to r modulo t. Using Wright's circle method, we derive an asymptotic for Dk×(r,t;n) as n→∞ when k,t are coprime. The main term of this asymptotic does not depend on r, and so, in a weak asymptotic sense, the parts are equidistributed among congruence classes. However, inspection of the lower order terms indicates a bias towards different congruence classes modulo t. This induces an ordering on the congruence classes modulo t, which we call the k-indivisible ordering. We prove that for k≥6(t2−1)π2 the k-indivisible ordering matches the natural ordering. We also explore the properties of these orderings when k<6(t2−1)π2.

Verbalization of comparison in Platon Oyunsky's heroic epic "Djuluruyar Nyurgun Bootur" and in the Altai epic "Maadai Kara"

The article considers the ways of expressing comparative relations in the Yakut and Altai heroic epics. The related Yakut and Altaic languages are currently being actively studied in comparative terms in order to identify specific differences. The comparative construction was previously studied in the Yakut language by Yu. I. Vasilyev, theoretical coverage was given by E. I. Ubryatova; in the Altai language the comparative construction was specially studied by L. N. Tybykova. The material of the study was the Yakut heroic epic "Djuluruyar Nyurgun Bootur" ("Nurgun Botur the Swift") and the Altai epic "Maadai Kara".

A validation of the Dutch version of the Awareness of Narrative Identity Questionnaire (ANIQ-NL).

Individuals build a narrative identity through the construction of an internalised, unfolding life story based on significant autobiographical memories. The current study validated a Dutch version of the Awareness of Narrative Identity Questionnaire (ANIQ-NL), which assesses how aware individuals are of having a narrative identity as well as their perception of the global coherence within their autobiographical memories, specifically, in terms of temporal ordering, causal connections and thematic integration. The questionnaire was administered to 541 adults (65.1% female, Mage = 34.09, SDage = 15.04, age range = 18-75). The results of a confirmatory factor analysis provided evidence for a four-factor structure, consisting of awareness and the three coherence subscales. The factor loadings of the items varied between .67 and .96. Moreover, the ANIQ-NL subscales showed good to excellent internal consistency, with Cronbach's alphas ranging from .86 to .96. Furthermore, higher levels of perceived autobiographical memory coherence were found to be significantly correlated to lower levels of depression, anxiety, and stress symptoms. The ANIQ-NL was determined to be a valid and reliable tool to measure narrative identity awareness and perceived narrative coherence. Future research could utilise the ANIQ-NL to further investigate the role of narrative identity in psychological well-being.

Optical rectification Hall effect in a one-dimensional grating

We observe a transverse optical rectification current enhanced by surface plasmon polaritons in a one-dimensional gold thin film with a grating whose unit cell is asymmetric. In the linear regime, momentum transfer from incident laser light in one plane of incidence cannot yield an electrical current in the transverse direction. We show that a nonlinear system can cross-couple coordinates and lead to a transverse photocurrent despite no linear momentum transfer in the transverse direction. Nonlinear effects can be described by higher order terms in the polarization density expansion, which relates the polarization to the electric fields in the system, via linear and higher-order susceptibility tensor coefficients. We modify this expression with a phenomenological term to explain the counterintuitive observations.

Identification of the time-dependent lowest term in a fourth order in time partial differential equation

In this article, identification of the time-dependent lowest term in a fourth order in time partial differential equation (PDE) from knowledge of a boundary measurement is studied by means of contraction mapping.

Exponential densities and compound Poisson measures

AbstractWe prove estimates at infinity of convolutions and densities of the corresponding compound Poisson measures for a class of radial decreasing densities on , , which are not convolution equivalent. Existing methods and tools are limited to the situation in which the convolution is comparable to initial density at infinity. We propose a new approach, which allows one to break this barrier. We focus on densities, which are products of exponential functions and smaller order terms—they are common in applications. In the case when the smaller order term is polynomial, estimates are given in terms of the generalized Bessel function. Our results can be seen as the first attempt to understand the intricate asymptotic properties of the compound Poisson and more general infinitely divisible measures constructed for such densities.

Molecular engineering of technologically relevant surfaces - carboxylic acids on naturally oxidized aluminum

Aluminum is a versatile, yet inexpensive metal that, when covered by oxide layer, might be employed as a gate dielectric in OFET devices, which carrier mobility could be enhanced by functionalization of dielectric by aliphatic carboxylic acid self-assembled monolayer (SAM). Although the organization of such SAMs plays an important role for the OFET performance, no systematical analysis of the impact of the preparation conditions on the quality of the carboxylate SAMs on aluminum oxide has been conducted so far, to the best of our knowledge. In the current work, we analyze, by the example of heptadecanoic acid SAM, the influence of the three crucial factors (i.e., type of solvent, immersion time, and incubation temperature) on the quality of the monolayer prepared by the standard immersion procedure. Several complementary techniques are combined to demonstrate a critical role of solvent choice in terms of monolayer order, orientation, thickness, and wettability. The results indicate in particular that the high solubility hinders the creation of high-quality SAMs, probably due to the solvent molecules incorporation into the monolayer. As a result of this study, we propose and rationalize a set of parameters enabling to obtain densely packed and well-ordered carboxylate SAMs on naturally oxidized aluminum.

A Special Relativistic Exploitation of the Second Law of Thermodynamics and Its Non-Relativistic Limit.

A thermodynamic process is a solution of the balance equations fulfilling the second law of thermodynamics. This implies restrictions on the constitutive relations. The most general way to exploit these restrictions is the method introduced by Liu. This method is applied here, in contrast to most of the literature on relativistic thermodynamic constitutive theory, which goes back to a relativistic extension of the Thermodynamics of Irreversible Processes. In the present work, the balance equations and the entropy inequality are formulated in the special relativistic four-dimensional form for an observer with four-velocity parallel to the particle current. The restrictions on constitutive functions are exploited in the relativistic formulation. The domain of the constitutive functions, the state space, is chosen to include the particle number density, the internal energy density, the space derivatives of these quantities, and the space derivative of the material velocity for a chosen observer. The resulting restrictions on constitutive functions, as well as the resulting entropy production are investigated in the non-relativistic limit, and relativistic correction terms of the lowest order are derived. The restrictions on constitutive functions and the entropy production in the low energy limit are compared to the results of an exploitation of the non-relativistic balance equations and entropy inequality. In the next order of approximation our results are compared to the Thermodynamics of Irreversible Processes.