Topological Solutions Research Articles

Topological black hole in the theory with nonminimal derivative coupling with power-law Maxwell field and its thermodynamics

We obtain topological black hole solutions in scalar-tensor gravity with nonminimal derivative coupling between scalar and tensor components of gravity and power-law Maxwell field minimally coupled to gravity. The obtained solutions can be treated as a generalization of previously derived charged solutions with standard Maxwell action \cite{Feng_PRD16}. We examine the behaviour of obtained metric functions for some asymptotic values of distance and coupling. To obtain information about singularities of the metrics we calculate Kretschmann scalar. We also examine the behaviour of gauge potential and show that it is necessary to impose some constraints on parameter of nonlinearity in order to obtain reasonable behaviour of the filed. The next part of our work is devoted to the examination of black hole's thermodynamics. Namely we obtain black hole's temperature and investigate it in general as well as in some particular cases. To introduce entropy we use well known Wald procedure which can be applied to quite general diffeomorphism-invariant theories. We also extend thermodynamic phase space by introducing thermodynamic pressure related to cosmological constant and as a result we derive generalized first law and Smarr relation. The extended thermodynamic variables also allow us to construct Gibbs free energy and its examination gives important information about thermodynamic stability and phase transitions. We also calculate heat capacity of the black holes which demonstrates variety of behaviour for different values of allowed parameters.

Topology optimization for minimizing the maximum temperature of transient heat conduction structure

In this paper, a topology optimization model is proposed for transient heat conduction structure design. In this model, a new performance index, named as the Regional Temperature Control Function (RTCF), was introduced as the objective function for representing the maximum temperature of specific areas during the whole working time, in this way the effect of the transient heat conduction on the topology is considered. An analytical expression is derived for the sensitivity analysis. Numerical examples demonstrate that the optimized topological solutions of the transient heat conduction structure exhibit the remarkable transient effect. That is to say, the optimal topology is closely related to the working time, and the different working time will lead to completely different topology designs for the same problem. Results also indicate that the proposed topology optimization model can exactly reflect the transient effect and achieve satisfactory topological solutions. In addition, compared with the transient thermal compliance as the objective function, the proposed RTCF can gain the design results with the obvious decrease of maximum temperature, which also implicates that the proposed topology optimization model for transient heat conduction structures is highly effective.

Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations

This paper uses the Ansatz method to solve for exact topological soliton solutions to sine-Gordon type equations. Single, double, and triple sine-Gordon and sine-cosine-Gordon equations are investigated along with dispersive and highly dispersive variations. After these solutions are found, strong perturbations are added to each equation and the new solutions are found. In solving both the perturbed and unperturbed sine-Gordon type equations, constraints are imposed on the parameters. The novel contributions of the authors are the soliton solutions to the strongly perturbed sine-Gordon equation and its variations. These results are important to the study of Josephson junctions, crystal dislocations, ultra-short optical pulses, relativistic field theory, and elementary particles.

The affective factors on the uncertainty in the collisions of the soliton solutions of the double field sine-Gordon system

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in 1+1 dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will be shown numerically, during collisions between solitons, there will be an uncertainty which originates from the amount of the maximum amplitude and arbitrary initial phases of the trapped wave packets.

On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering

The studies of the dynamic behaviors of nonlinear models arising in ocean engineering play a significant role in our daily activities. In this study, we investigate the coupled Boussinesq equation which arises in the shallow water waves for two-layered fluid flow. The modified exp $$(-\varphi (\zeta ))$$ -expansion function method is utilized in reaching the solutions to this equation such as the topological kink-type soliton and singular soliton solutions. The interesting 2D and 3D graphics of the obtained analytical solutions in this study are presented. Via one of the reported analytical solutions, the finite forward difference method is used in obtaining the approximate numerical and exact solutions to this equation. The Fourier–Von Neumann analysis is used in checking the stability of the used numerical method with the studied model. The $$L_{2}$$ and $$L_{\infty }$$ error norms are computed. We finally present a comprehensive conclusion to this study.

Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints

Abstract With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.

Manipulating graphene kinks through positive and negative radiation pressure effects

We introduce an idea of experimental verification of the counterintuitive negative radiation pressure effect in some classical field theories by means of buckled graphene. In this effect, a monochromatic plane wave interacting with topological solutions pulls these solutions towards the source of radiation. Using extensive molecular dynamics simulations, we investigate the traveling wave-induced motion of kinks in buckled graphene nanoribbons. It is shown that depending on the driving source frequency, amplitude and direction, the kink behavior varies from attraction to repulsion (the negative and positive radiation pressure effects, respectively). Some preliminary explanations are proposed based on the analogy to certain field theory models. Our findings open the way to a new approach to motion control on the nanoscale.

A Survey of Topology Control in Wireless Networks

Wireless Sensor Networks (WSNs)/Mobile Ad hoc Networks and Delay-tolerant Networks have many applications in recent years. Topology control is one of the most important research topics in wireless networks. It not only can prolong the lifetime of the network but also reduce the signal interference. Therefore, the research of topology control is of great significance. This paper analyzes and summarizes the main directions and research results of topology control problem of wireless networks in recent years, at the same time classifies and summarizes the topological control solutions in wireless sensor / mobile ad-hoc networks and delay tolerant networks, finally, points out the shortcomings and future research directions.

Connected door spaces and topological solutions of equations

The connected door space is an enigmatic topological space in which every proper nonempty subset is either open or closed, but not both. This paper provides an elementary proof of the classification theorem of connected door spaces. More importantly, we show that connected door topologies can be viewed as solutions of the valuation $f(A)+f(B)=f(A\cup B)+f(A\cap B)$ and the equation $f(A)+f(B)=f(A\cup B)$, respectively. In addition, some special solutions, which can be regarded as a union of connected door spaces, are provided.

Novel connection between lump-like structures and quantum mechanics

This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar field theories that support both lumps and kinks, with the corresponding stability investigation giving rise to new physical systems. Very interestingly, we find models that support stable topological solutions, with the stability potential being able to support a tower of non-negative bound states, generating distinct families of potentials of current interest to quantum mechanics. We also describe models where the lump-like solutions give rise to stability potentials that have the shape of a double-well.

The skyrmion-bubble transition in a ferromagnetic thin film

Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field.

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

Here we study the global existence of “hairy” dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case. We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for su(N). We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as |Λ| → ∞. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the su(N) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date.

On the solitary wave solutions to the longitudinal wave equation in MEE circular rod

This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

The investigation of soliton solutions and conservation laws to the coupled generalized Schrödinger–Boussinesq system

This paper employed the principle of undetermined coefficients and Bernoulli sub-ODE methods to acquire the topological, non-topological, periodic wave and algebraic solutions of the coupled generalized Schrödinger–Boussinesq system (CGSBs). The concept of Lie point symmetry is applied to derive the point symmetries of the CSGE. The problem on nonlinear self-adjointness of the CSGE has not been solved in previous time. In the present paper, we solve this problem and find an explicit form of the differential substitution providing the nonlinear self-adjointness. Then we use this fact to construct a set of conserved vectors using the classical symmetries admitted by the equation and the general conservation laws (Cls) theorem presented by Ibragimov. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.

Kinklike structures in models of the Dirac–Born–Infeld type

The present work investigates several models of a single real scalar field, engendering kinetic term of the Dirac–Born– Infeld type. Such theories introduce nonlinearities to the kinetic part of the Lagrangian, which presents a square root restricting the field evolution and including additional powers in derivatives of the scalar field, controlled by a real parameter. In order to obtain topological solutions analytically, we propose a first-order framework that simplifies the equation of motion ensuring solutions that are linearly stable. This is implemented using the deformation method, and we introduce examples presenting two categories of potentials, one having polynomial interactions and the other with nonpolynomial interactions. We also explore how the Dirac–Born–Infeld kinetic term affects the properties of the solutions. In particular, we note that the kinklike solutions are similar to the ones obtained through models with standard kinetic term and canonical potential, but their energy densities and stability potentials vary according to the parameter introduced to control the new models.

Topological solutions in the Maxwell-Chern-Simons model with anomalous magnetic moment

In this paper, we consider a Maxwell-Chern-Simons model with anomalous magnetic moment. Our main goal is to show the existence and uniqueness of topological type solutions to this problem on a flat two torus for any configuration of vortex points. Moreover, we also discuss about the stability of topological solutions.

Scalable topological forwarding and routing policies in RINA‐enabled programmable data centers

AbstractGiven the current expansion of cloud computing, the expected advent of the Internet of Things, and the requirements of future fifth‐generation network infrastructures, significantly larger pools of computational and storage resources will soon be required. This emphasizes the need for more scalable data centers that are capable of providing such an amount of resources in a cost‐effective way. A quick look into today's commercial data centers shows that they tend to rely on variations of well‐defined leaf‐spine/Clos data center network (DCN) topologies, offering low latency, ultrahigh bisectional bandwidth, and enhanced reliability against concurrent failures. However, DCNs are typically restricted by the use of the Transmission Control Protocol/Internet Protocol (TCP/IP) suite, thus suffering limited routing scalability. In this work, we study the benefits that replacing TCP/IP with the recursive internetwork architecture (RINA) can bring into commercial DCNs, focusing on forwarding and routing scalability. We quantitatively evaluate the benefits that RINA solutions can yield against those based on TCP/IP and highlight how, by deploying RINA, topological routing solutions can improve even more the efficiency of the network. To this goal, we propose a rule‐and‐exception forwarding policy tailored to the characteristics of several DCN variants, enabling fast forwarding decisions with merely neighbors' information. Upon failures, few exceptions are necessary, whose computation can also profit from the known topology. Extensive numerical results show that the proposed policy requirements depend mainly on the number of neighbors and concurrent failures in the DCN rather than its size, dramatically reducing the amount of forwarding and routing information stored at DCN nodes.

Existence of topological multi-string solutions in Abelian gauge field theories

In this paper, we consider a general form of self-dual equations arising from Abelian gauge field theories coupled with the Einstein equations. By applying the super/subsolution method, we prove that topological multi-string solutions exist for any coupling constant, which improves previously known results. We provide two examples for application: the self-dual Einstein-Maxwell-Higgs model and the gravitational Maxwell gauged O(3) sigma model.

Bubbling mixed type solutions of the SU(3) models on a torus

We consider a nonlinear elliptic system arising in the study of the SU(3) Chern-Simons model on a two-dimensional flat torus Ω. Solutions of this SU(3) Chern Simons system could be classified as topological, mixed-type, and non-topological solutions. In this paper, we succeed to construct bubbling mixed type solutions. This is the first result for such example in the literature. The analysis for the existence of such solution provides some important insights for us to develop the asymptotic analysis of classifying all mixed-type solution.