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Obstructive sleep apnea (OSA) is related to increased risk of cardiovascular disease. Ferroptosis is a form of programmed cell death characterized by iron overload and plays critical roles in myocardial injury. This study aimed to investigate the role of ferroptosis in intermittent hypoxia (IH)-induced myocardial injury involving endoplasmic reticulum stress (ERS).AC16 human cardiomyocytes were exposed to IH or normoxia conditions. Mice were randomly grouped as follows: normal control (NC), IH, ferrostatin-1 + IH (FIH), and N-acetylcysteine + IH (AIH). The mRNA levels of GPX4, xCT, FTH1, and FACL4 in AC16 cells were detected by qRT-PCR. The protein levels of GPX4, xCT, NOX4, ATF4, CHOP, Bcl-2, and Bax in myocardial tissue were detected by Western blot analysis.The mRNA expression levels of GPX4 and xCT in AC16 cells were significantly lower in IH group than that of NC group. In IH mice, myocardial tissues were injured accompanied by increased level of ferroptosis and ERS. Inhibition of ferroptosis and treatment of N-acetylcysteine reduced ERS and myocardial injury in mice exposed to IH. In addition, compared to ferrostatin-1, N-acetylcysteine exerted a greater effect in relieving IH-induced myocardial damage and ERS.Ferroptosis was involved in IH-related myocardial injury accompanied by the activation of ERS. Inhibition of ferroptosis and acetylcysteine treatment alleviated IH-related myocardial injury, which may be a potential target for therapeutic approaches to OSA-induced myocardial injury.

We derive the equations of motion governing static dyonic matters, described in terms of two real scalar fields, in nonlinear electrodynamics of the Born--Infeld theory type. We then obtain exact finite-energy solutions of these equations in the quadratic and logarithmic nonlinearity cases subject to dyonic point-charge sources and construct dyonically charged black holes with relegated curvature singularities. In the case of quadratic nonlinearity, which is the core model of this work, we show that dyonic solutions enable us to restore electromagnetic symmetry, which is known to be broken in non-dyonic situations by exclusion of monopoles. We further demonstrate that in the context of k-essence cosmology the nonlinear electrodynamics models possess their own distinctive signatures in light of the underlying equations of state of the cosmic fluids they represent. In this context, the quadratic and logarithmic models are shown to resolve a density-pressure inconsistency issue exhibited by the original Born--Infeld model k-essence action function as well as by all of its fractional-powered extensions. Moreover, it is shown that the quadratic model is uniquely positioned to give rise to a radiation-dominated era in the early universe among all the polynomial models and other examples considered., 38 pages, 1 figure

Purpose Chronic intermittent hypoxia (CIH) causes lung injury but the mechanism is unclear. Ferroptosis is a novel form of programmed cell death. In this research, we attempted to explore the role of ferroptosis in CIH-induced lung injury both in vitro and in vivo. Methods Sprague-Dawley rats were randomly separated into control group, CIH group and CIH + ferrostatin-1 group (CIH + Fer-1). Rats in the CIH group and CIH + Fer-1 group were exposed to intermittent hypoxia for 12 weeks. Human bronchial epithelial cell line (BEAS-2B) was cultivated for 24 h in either conventional culture medium or under CIH conditions. Fer-1 was applied to observe its treatment effects. Histological changes were evaluated by Hematoxylin–eosin (HE) staining and masson staining. The expression levels of Acyl-CoA synthetase long-chain family member 4 (ACSL4), glutathione peroxidase 4 (GPX4), interleukin-6 (IL-6) and tumour necrosis factor α (TNFα) were detected via qRT-PCR or Western blot. Cell counting kit-8 (CCK-8) was used to assess cell viability. The apoptotic rate and reactive oxygen species (ROS) was calculated by flow cytometry. Results Histology showed that CIH treatment induced lung injury and pulmonary fibrosis in lung tissue. After Fer-1 treatment, the pathological changes caused by CIH alleviated. The mRNA and protein levels of GPX4 decreased significantly in lung tissues of CIH-treated rats and BEAS-2B, (p p p p p Conclusions Ferroptosis occurred in CIH-induced lung injury, both in vitro and in vivo. The ferroptosis inhibitor Fer-1 alleviated cell injury and ferroptosis in CIH-treated BEAS-2B and lung tissues of rats.

Developing efficient hydrogen oxidation reaction (HOR) electrocatalysts in alkaline media is of great significance for anion exchange membrane fuel cells. Herein, we report the synthesis of hollow colloidosomes composed of Ru nanocrystals based on a novel gas/liquid interface self-assembly strategy. Structural characterizations reveal that much defects are present in the building block (Ru nanocrystals) of Ru colloidosomes. Theoretical calculations suggest that the defects in the Ru structure can optimize the adsorption binding energy of reaction intermediates for the HOR. Benefiting from the assembled colloidosome and optimized electronic structure, the Ru colloidosomes exhibit remarkable HOR catalytic performance in alkaline media with a mass activity higher than that of benchmark Pt/C. Our work may shed new light on the rational design of advanced electrocatalysts with an assembled structure for energy-related applications.

Black hole solutions to the Einstein equations coupled with the Born--Infeld electromagnetism associated with generalized nonlinear electrodynamics, carrying both electric and magnetic charges, often referred to as dyonically charged black holes, of finite energies, are constructed. These solutions give rise to relegated curvature singularities at the center of the matter sources of the black holes and approach the classical Reissner--Nordstrom black hole asymptotically., 27 pages

The incidence of Alzheimer’s disease (AD) is increasing year by year, which brings great challenges to human health. However, the pathogenesis of AD is still unclear, and it lacks early diagnostic targets. The entorhinal cortex (EC) is a key brain region for the occurrence of AD neurodegeneration, and neuroinflammation plays a significant role in EC degeneration in AD. This study aimed to reveal the close relationship between inflammation-related genes in the EC and AD by detecting key differentially expressed genes (DEGs) via gene function enrichment pathway analysis. GSE4757 and GSE21779 gene expression profiles of AD were downloaded from the Gene Expression Omnibus (GEO) database. R language was used for the standardization and differential analysis of DEGs. Then, significantly enriched Gene Ontology (GO) terms and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways were analyzed to predict the potential biological functions of the DEGs. Finally, the significant expressions of identified DEGs were verified, and the therapeutic values were detected by a receiver operating characteristic (ROC) curve. The results showed that eight up-regulated genes (SLC22A2, ITGB2-AS1, NIT1, FGF14-AS2, SEMA3E, PYCARD, PRORY, ADIRF) and two down-regulated genes (AKAIN1, TRMT2B) may have a potential diagnostic value for AD, and participate in inflammatory pathways. The area under curve (AUC) results of the ten genes showed that they had potential diagnostic value for AD. The AUC of PYCARD was 0.95, which had the most significant diagnostic value, and it is involved in inflammatory processes such as the inflammasome complex adaptor protein. The DEGs screened, and subsequent pathway analysis revealed a close relationship between inflammation-related PYCARD and AD, thus providing a new basis for an early diagnostic target for AD.

The introduction of heteroatoms is one of the most important ways to modulate the intrinsic electronic structure of electrocatalysts to improve their catalytic activity. However, for transition metal chalcogenides with highly symmetric crystal structure (HS-TMC), the introduction of heteroatoms, especially those with large atomic radius, often induces large lattice distortion and vacancy defects, which may lead to structural phase transition of doped materials or structural phase reconstruction during the catalytic reaction. Such unpredictable situations will make it difficult to explore the connection between the intrinsic electronic structure of doped catalysts and catalytic activity. Herein, taking thermodynamically stable cubic CoSe2 phase as an example, we demonstrate that nitrogen incorporation can effectively regulate the intrinsic electronic structure of HS-TMC with structural phase stability and thus promote its electrocatalytic activity for the hydrogen evolution activity (HER). In contrast, the introduction of phosphorus can lead to structural phase transition from cubic CoSe2 to orthorhombic phase, and the structural phase of phosphorus-doped CoSe2 is unstable for HER.

A series of quantization identities are established for static vortex solutions governed by the Born--Infeld type actions. These identities are of a universal nature which are indifferent to the details of the models and provide refined descriptions of divergent energetic quantities., 22 pages, 1 figure, 2 tables of numerical data

It is shown that the Born--Infeld nonlinear electrodynamics with a polynomial type nonlinearity accommodates finite-energy electric point charges but rejects finite-energy magnetic point charges, or monopoles, thereby spelling out an electromagnetic asymmetry. Moreover, it is demonstrated, in a systematic way, that the curvature singularities of finite-energy charged black holes in the context of the Born--Infeld theory may effectively be relegated or in some cases removed under a critical mass-energy condition, which has been employed successfully in earlier concrete studies. Furthermore, it is illustrated through numerous examples considered here that, when adapted to describe scalar-wave matters known as k-essences, the Born--Infeld formalism provides a fertile ground for cosmological applications, including achieving accelerated dark-energy expansions and acquiring adequate field-theoretical realizations of the equations of state of various cosmic fluid models., Comment: 76 pages, 2 figures. Citations to literature are updated and some corrections are made

We show that the closed-form monotone solution linking two different vacuum states, for the exterior Yang--Mills wave equation over the extremal Reissner--Nordstr\"{o}m spacetime found in a recent work of Bizo\'{n} and Kahl, is the unique solution to an associated domain-wall type energy minimization problem. We also derive the accompanying interior Yang--Mills wave equation within the same formalism. We obtain a few more closed-form solutions, regular and singular, among other solutions of oscillatory behavior, and discuss several interesting features of the solutions based on some energy consideration., Comment: 16 pages, 2 figure

We prove the existence of dark monopole solutions in a recently formulated Yang--Mills--Higgs theory model with technical features similar to the classical monopole problems. The solutions are obtained as energy-minimizing static spherically symmetric field configurations of unit topological charge. We overcome the difficulty of recovering the full set of boundary conditions by a regularization method which may be applied to other more complicated problems concerning monopoles and dyons in non-Abelian gauge field theories. Furthermore we show in a critical coupling situation that an explicit BPS solution may be used to provide energy estimates for non-BPS monopole solutions. Besides, in the limit of infinite Higgs coupling parameter, although no explicit construction is available, we establish an existence and uniqueness result for a monopole solution and obtain its energy bounds., Comment: 20 pages, 1 figure. Revised version to appear in Nuclear Physics B

We establish a 3-parameter family of integral identities to be used on a class of theories possessing solitons with spherical symmetry in $d$ spatial dimensions. The construction provides five boundary charges that are related to certain integrals of the profile functions of the solitons in question. The framework is quite generic and we give examples of both topological defects (like vortices and monopoles) and topological textures (like Skyrmions) in 2 and 3 dimensions. The class of theories considered here is based on a kinetic term and three functionals often encountered in reduced Lagrangians for solitons. One particularly interesting case provides a generalization of the well-known Pohozaev identity. Our construction, however, is fundamentally different from scaling arguments behind Derrick's theorem and virial relations. For BPS vortices, we find interestingly an infinity of integrals simply related to the topological winding number., Comment: LaTeX: 35 pages, 1 figure; V2: comment added and typos corrected

Previous studies have indicated that social evaluations rely heavily on the outcome of an actor's behavior toward a recipient. These studies focused on interactions in which two agents are connected by an external goal (i.e., object-mediated social interaction) and revealed that the intent behind an action has a privileged role in evaluating the valence of a social interaction. The current study investigated whether the intent behind an action influences evaluation of contingent social interactions wherein one agent responds to another without referring to a specific target. To clarify this, we operationalized intent as harmful or harmless when one agent hit another (i.e., recipient), and manipulated the action's outcome by determining to what extent it changed the recipient's state (i.e., falling down or moving slightly). Results showed that in contingent interactions with both direct launching (i.e., the actor directly caused the change) and extended launching (i.e., the actor caused the change through a mediated block), when the action significantly affected the recipient, the agents were evaluated as having a more negative social interaction than when the influence was small; this effect was independent of the intent behind the action. Such findings demonstrated that evaluations of contingent social interactions are primarily influenced by an actor's causal role in the outcome, not the intent behind an action. This null effect of intent when evaluating social interaction contrasts with findings on object-mediated social interaction, which is consistent with human social evaluations relying on two dissociable systems: causal and intentional components.

In this note an analytic integration is obtained for the differential equation governing the scalar-field-dependent mass in a hairy binary black hole model, in the context of the Einstein--Maxwell--dilation theory, which gives a closed-form formula-level description of the mass function. We also identify a particular solution which attracts all solutions of the mass-governing equation exponentially rapidly in large-dilaton-field limit., 16 pages, 5 figures, to appear

In this paper we first formulate a dually gauged harmonic map model, suggested from a product Abelian Higgs field theory arising in impurity-inspired field theories, and obtain a new BPS system of equations governing coexisting vortices and antivortices, which are topologically characterized by the first Chern class of the underlying Hermitian bundle and the Thom class of the associated dual bundle. We then establish existence and uniqueness theorems for such vortices. For the equations over a compact surface, we obtain necessary and sufficient conditions for the existence of solutions. For the equations over the full plane, we obtain all finite-energy solutions. Besides, we also present precise expressions giving the values of various physical quantities of the solutions, including magnetic charges and energies, in terms of the total numbers of vortices and antivortices, of two species, and the coupling parameters involved., 30 pages, 1 figure

We present analytic and computational studies of the dynamical behavior of an undamped electrostatic MEMS actuator with one-degree of freedom subject to a Casimir force. In such a situation, the well-known mathematical difficulty associated with an inverse quadratic term due to a Coulomb force is supplemented with an inverse quartic term due to the joint application of a Casimir force. We show that the small Coulomb and Casimir force situations, described by sufficiently low values of two positive parameters, λ and μ, respectively, are characterized by one-stagnation-point periodic motions and there exists a unique critical pull-in curve in the coordinate quadrant beyond which a finite-time touch down or collapse of the actuator takes place. We demonstrate how to locate and approximate the pull-in curve. When mechanical nonlinearity such as that due to the presence of a cubic elastic force term is considered in the equation of motion, we show that a similar three-phase oscillation-pull-in-finite-time-touchdown phenomenon occurs and that pull-in curves are actually enhanced or elevated by nonlinear elasticity. Furthermore, we compute solutions of the MEMS wave equations and show that the same characteristic phenomena of subcritical periodic motions and loss of periodicity of motion and onset of a critical pull-in curve occur as one increases the levels of the Coulomb and Casimir forces as in the one-degree-of-freedom case.

It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations., Comment: 28 pages

Explicit expressions for the bending angle of light deflection arising from phenomenologically deformed black-hole metrics, subject to possible weak and strong quantum gravity effects, respectively, are obtained, by a highly effective method. The accuracy and effectiveness of these expressions are then illustrated by numerically solving the differential equation governing the deflection angle directly in the weak quantum effect situation., 18 pages. Modification and improvement are made to the previous version. Title is modified. To appear

Though distance perception feeds the fundamental input that constructs a visual structure of the world, the suggestion has been made that it is constrained by this constructed structure. Instead of focusing on the physically defined structure, this study investigates whether and how social relations, especially the quality of social interaction (how individuals interact) rather than its content (what type of social interaction), precisely influences distance perception. The quality of social interaction was framed as an actor’s intent and incurred outcome regarding another individual, whether helpful or harmful. Through visual animations, intent was operationalized as an agent’s (i.e., actor’s) intentional or unintentional act having an influence on another agent (i.e., affectee). Two experiments were conducted. In Experiment 1, the act was helpful, resulting in small or great beneficial consequences to the affectee. In Experiment 2, the act was harmful and resulted in small or great losses to the affectee. We found that when the help or harm had a large effect on others (the great-benefits or great-losses conditions), distance was perceived as shorter than when help or harm was minor, and the actor’s intent did not affect distance perception. This suggests that, regardless of the type of social interaction, distance perception is mainly influenced by the outcome of an act not by the actor’s intent. It implies that the perceived quality of social interaction creates a social constraint on distance perception. These findings are consistent with the idea that the intent and outcome of an action are assessed differently, and they help us understand how social relation penetrates the perceptual system.

The Helfrich bending energy plays an important role in providing a mechanism for the conformation of a lipid vesicle in theoretical biophysics, which is governed by the principle of energy minimization over configurations of appropriate topological characteristics. We will show that the presence of a quantity called the spontaneous curvature obstructs the existence of a minimizer of the Helfrich energy over the set of embedded ring tori. Besides, despite the well-realized knowledge that lipid vesicles may present themselves in a variety of shapes of complicated topology, there is a lack of topological bounds for the Helfrich energy. To overcome these difficulties, we consider a general scale-invariant anisotropic curvature energy that extends the Canham elastic bending energy developed in modeling a biconcave-shaped red blood cell. We will show that, up to a rescaling of the generating radii, there is a unique minimizer of the energy over the set of embedded ring tori, in the entire parameter regime, which recovers the Willmore minimizer in its Canham isotropic limit. We also show how elevated anisotropy favors energetically a clear transition from spherical-, to ellipsoidal-, and then to biconcave-shaped surfaces, for a lipid vesicle. We then establish some genus-dependent topological lower and upper bounds for the anisotropic energy. Finally, we derive the shape equation of the generalized bending energy, which extends the well-known Helfrich shape equation., 29 pages and 2 figures. Revised and updated version for Physical Review E

Using numerical simulations, we examine the dynamics of driven two-dimensional bidisperse disks flowing over quenched disorder. The system exhibits a series of distinct dynamical phases as a function of applied driving force and packing fraction including a phase separated state as well as a smectic state with liquid like or polycrystalline features. At low driving forces, we find a clogged phase with an isotropic density distribution, while at intermediate driving forces the disks separate into bands of high and low density with either liquid like or polycrystalline structure in the high density bands. In addition to the density phase separation, we find that in some cases there is a fractionation of the disk species, particularly when the disk size ratio is large. The species phase separated regimes form a variety of patterns such as large disks separated by chains of smaller disks. Our results show that the formation of laning states can be enhanced by tuning the ratio of disk radius of the two species, due to the clumping of small disks in the interstitial regions between the large disks., Comment: 15 pages, 18 figures

It is shown that the gap solution and critical transition temperature are significantly enhanced by doping in a recently developed BCS formalism for graphene superconductivity in such a way that positive gap and transition temperature both occur in arbitrary pairing coupling as far as doping is present. The analytic construction of the BCS gap and transition temperature offers highly effective globally convergent iterative methods for the computation of these quantities. A series of numerical examples are presented as illustrations consolidating the analytic understanding achieved., 21 pages, 8 figures

Gravitational light deflection is known as one of three classical tests of general relativity and the angle of deflection may be computed explicitly using approximate or exact solutions describing the gravitational force generated from a point mass. In various generalized gravity theories, however, such explicit determination is often impossible due to the difficulty with obtaining an exact expression for the deflection angle. In this work, we present some highly effective globally convergent iterative methods to determine the angle of semiclassical gravitational deflection in higher- and infinite-derivative formalisms of quantum gravity theories. We also establish the universal properties that the deflection angle always stays below the classical Einstein angle and is a strictly decreasing function of the incident photon energy, in these formalisms., Comment: 32 pages, 8 figures

We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the ${\cal N}=2$ supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern--Simons dynamics at dual levels and realized as the solutions of a system of elliptic equations with exponential nonlinearity over two-dimensional domains. In the full plane situation, our method utilizes a minimization approach, and in the doubly periodic situation, we employ an-inequality constrained minimization approach. In the latter case, we also obtain sufficient conditions under which we show that there exist at least two gauge-distinct solutions for any prescribed distribution of vortices. In other words, there are distinct solutions with identical vortex distribution, energy, and electric and magnetic charges., Comment: 39 pages

Regarding the Skyrme–Faddeev model on R 3 as a CP 1 sigma model, we propose C P n sigma models on R 2 n + 1 as generalisations which may support finite energy Hopfion solutions in these dimensions. The topological charge stabilising these field configurations is the Chern–Simons charge, namely the volume integral of the Chern–Simons density which has a local expression in terms of the composite connection and curvature of the CP n field. It turns out that subject to the sigma model constraint, this density is a total divergence. We prove the existence of a topological lower bound on the energy, which, as in the Vakulenko–Kapitansky case in R 3 , is a fractional power of the topological charge, depending on n . The numerical construction of the simplest ring shaped un-knot Hopfion on R 5 is also discussed.

A fundamental subject in ecology is to understand how an ecosystem responds to its environmental changes. The purpose of this paper is to study the desertification and vegetation pattern formation phenomena and understand the dependence of the biomass density B of vegetation on the level of available environmental water resources, controlled by a water supply rate parameter R , which is governed by a coupled system of nonlinear parabolic equations in a mathematical model proposed recently by Shnerb, Sarah, Lavee, and Solomon. It is shown that, when R is below the death rate μ of the vegetation in the absence of water, the solution evolving from any initial state approaches exponentially fast the desert state characterized by B = 0 ; when R is above μ , the solution evolves into a green vegetation state characterized by B ⁄ → 0 as time t → ∞ . In the flower-pot limit where the system becomes a system of ordinary differential equations, it is shown that nontrivial periodic vegetation states exist provided that the water supply rate R is a periodic function and maintains a suitable average level. Furthermore, some conservation laws relating the asymptotic values of the vegetation biomass B and available water density W are also obtained.

By means of variational methods, in this paper, we establish sharp existence results for solutions of the master equations governing ‘fractional multiple vortices.’ In the doubly periodic situation, the conditions for existence are both necessary and sufficient and give the upper bounds for the vortex numbers in terms of the size of the periodic cell domain. In the planar situation, there is no restriction on the vortex numbers. In both situations, the solutions are uniquely determined by the prescribed locations and the local winding numbers of the vortices.

A known feature of electrically charged Reissner-Nordstr\"om-anti-de Sitter planar black holes is that they can become unstable when considered as solutions of Einstein--Yang-Mills theory. The mechanism for this is that the linearized Yang-Mills equations in the background of the Reissner-Nordstr\"om (RN) black holes possess a normalizable zero mode, resulting in non-Abelian (nA) magnetic clouds near the horizon. In this work we show that the same pattern may occur also for asymptotically flat RN black holes. Different from the anti-de Sitter case, in the Minkowskian background the prerequisite for the existence of the nA clouds is $i)$ a large enough gauge group and $ii)$ the presence of some extra interaction terms in the matter Lagrangian. To illustrate this mechanism we present two specific examples, one in four and the other in five dimensional asymptotically flat spacetime. In the first case, we augment the usual $SU(3)$ Yang-Mills Lagrangian with higher order (quartic) curvature term, while for the second one we add the Chern-Simons density to the $SO(6)$ Yang-Mills system. In both cases, an Abelian gauge symmetry is spontaneously broken near a RN black hole horizon with the appearance of a condensate of nA gauge fields. In addition to these two examples, we review the corresponding picture for anti-de Sitter black holes. All these solutions are studied both analytically and numerically, existence proofs being provided for nA clouds in the background of RN black holes. The proofs use shooting techniques which are suggested by and in turn offer insights for our numerical methods. They indicate that, for a black hole of given mass, appropriate electric charge values are required to ensure the existence of solutions interpolating desired boundary behavior at the horizons and spatial infinity., Comment: 19 pages, 5 figures

A search is performed for heavy Majorana neutrinos (N) using an event signature defined by two like-sign charged leptons of the same flavour and two jets. The data correspond to an integrated luminosity of 5.0 inverse femtobarns of pp collisions at a centre-of-mass energy of 7 TeV collected with the CMS detector at the Large Hadron Collider. No excess of events is observed beyond the expected standard model background and therefore upper limits are set on the square of the mixing element, abs(V[ell N]) squared, for ell = e, mu, as a function of Majorana neutrino mass. These are the first direct upper limits on the heavy Majorana-neutrino mixing for m[N] > 90 GeV.

We prove the existence of electrically and magnetically charged particlelike static solutions, known as dyons, in the minimally gauged Skyrme model developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically symmetric, depend on two continuous parameters, and carry unit monopole and magnetic charges but continuous Skyrme charge and non-quantized electric charge induced from the 't Hooft electromagnetism. The problem amounts to obtaining a finite-energy critical point of an indefinite action functional, arising from the presence of electricity and the Minkowski spacetime signature. The difficulty with the absence of the Higgs field is overcome by achieving suitable strong convergence and obtaining uniform decay estimates at singular boundary points so that the negative sector of the action functional becomes tractable., 24 pages

Vortices in supersymmetric gauge field theory are important constructs in a basic conceptual phenomenon commonly referred to as the dual Meissner effect which is responsible for color confinement. Based on a direct minimization approach, we present a series of sharp existence and uniqueness theorems for the solutions of some non-Abelian vortex equations governing color-charged multiply distributed flux tubes, which provide an essential mechanism for linear confinement. Over a doubly periodic domain, existence results are obtained under explicitly stated necessary and sufficient conditions that relate the size of the domain, the vortex numbers, and the underlying physical coupling parameters of the models. Over the full plane, existence results are valid for arbitrary vortex numbers and coupling parameters. In all cases, solutions are unique., 38 pages, latex

Vortices in non-Abelian gauge field theory play essential roles in the mechanism of color confinement and are governed by systems of nonlinear elliptic equations of complicated structure. In this paper, we present a series of sharp existence and uniqueness theorems for multiple vortex solutions of the non-Abelian BPS equations over R 2 and on a doubly periodic domain. Our methods are based on calculus of variations which may be used to analyze more extended problems. The necessary and sufficient conditions for the existence of a unique solution in the doubly periodic situation are expressed in terms of physical parameters involved explicitly.

In this paper, we consider a system of non-Abelian multiple vortex equations governing coupled SU(N) and U(1) gauge and Higgs fields which may be embedded in a supersymmetric field theory framework. When the underlying domain is doubly periodic, we prove the existence and uniqueness of an n-vortex solution under a necessary and sufficient condition explicitly relating the domain size to the vortex number n and the Higgs boson masses. When the underlying domain is the full plane, we use a constructive approach to establish the existence and uniqueness of an n-vortex solution.

We prove the existence of a continuous family of finite-energy particle-like solutions in the coupled Georgi–Glashow–Skyrme model carrying both electric and magnetic charges, known as dyons. Due to the presence of electricity and the Minkowski spacetime signature, we need to solve a variational problem with an indefinite action functional. Our results show that, while the magnetic charge is uniquely determined by the topological monopole number, the electric charge of a solution can be arbitrarily prescribed in an open interval.

A general quantitative model for ontogenetic growth of organisms was derived by West et al. based on fundamental principles for the allocation of metabolic energy in which a universal parameterless growth curve was established in terms of the biomass ratio and a dimensionless biological time. This model was then extended by Guiot et al. to account for the growth of tumors in vivo in which the fractional scaling exponent p becomes a dynamic parameter depending on time t . In this paper, we present a method that may be used effectively to construct a generalized universal growth curve for such a growth law model with an arbitrary dynamically varying fractional exponent. As by-products of this method, we show that the assumption that a biological time variable flows forward in the universal curve allows us to predict the behavior of p with regard to the developmental stages of organisms characterized by body mass which is consistent with the findings of Guiot et al. based on biomedical data, and that, the universal curve is independent of the properties of p as a function of t . We also consider the situation when time increases discretely and the fractional scaling exponent is periodic. We observe the familiar, but superimposed, period-doubling and transition-to-chaos phenomenon.

In this paper, we prove the existence of finite-energy electrically and magnetically charged vortex solutions in the full Chern–Simons–Higgs theory, for which both the Maxwell term and the Chern–Simons term are present in the Lagrangian density. We consider both Abelian and non-Abelian cases. The solutions are smooth and satisfy natural boundary conditions. Existence is established via a constrained minimization procedure applied on indefinite action functionals. This work settles a long-standing open problem concerning the existence of dually charged vortices in the classical gauge field Higgs model minimally extended to contain a Chern–Simons term.

The presence of a fractional-exponent growth law relating knot energy and knot topology is known to be an essential characteristic for the existence of ‘ideal’ knots. In this paper, we show that the energy infimum E N stratified at the Hopf charge N of the knot energy of the Faddeev type induced from the Hopf fibration ( n ≥1) in general dimensions obeys the sharp fractional-exponent growth law , where the exponent p is universally rendered as , which is independent of the detailed fine structure of the knot energy but determined completely by the dimensions of the domain and range spaces of the field configuration maps.

We prove the existence of topological vortices in a relativistic self-dual Abelian Chern–Simons theory with two Higgs particles and two gauge fields through a study of a coupled system of two nonlinear elliptic equations over R2. We present two approaches to prove existence of solutions on bounded domains: via minimization of an indefinite functional and via a fixed point argument. We then show that we may pass to the full R2 limit from the bounded-domain solutions to obtain a topological solution in R2.

The nonlinear non-local elliptic equation governing the deflection of charged plates in electrostatic actuators is studied under the pinned and the clamped boundary conditions. Results concerning the existence, construction and approximation, and behaviour of classical and singular solutions with respect to the variation of physical parameters of the equation in various situations are presented.

In the context of static cosmic strings, the Einstein equations coupled to the Abelian Higgs model and the gauged σ-model reduce into a single equation, which directly relates the Gauss curvature of a Riemann surface hosting nontrivial geometry and gravitation to the energy density of the coupled matter-gauge sector. This equation gives rise to an equivalence relation between the topology of the Riemann surface and the topology of the complex line bundle which hosts and is determined by the physical interactions of the matter-gauge sector. The existence of solutions realizing a prescribed distribution of cosmic strings resembles the classical prescribed Gauss curvature problem. 1. Geometry, Physics, and Governing Equations Geometry, Physics, and the Einstein Equations. The basic principle that led Einstein to write down his fundamental equations for gravitation is that the geometry of spacetime which governs the gravitation in it is determined by the matter it contains. These equations may be viewed as the equations of motion of Received December 9, 2005. ∗This survey article is written based on a talk given at the conference Partial Differential Equations and Calculus of Variations in honor of Professors Robert Gulliver, Robert Hardt, and Leon Simon on the occasion of their 60th birthdays, Zhejiang University, Hangzhou, China, June 23–28, 2005.