Dimensional Nonlinear Model Research Articles

Critical net-baryon fluctuations in an expanding system

In this work we study the consequences of a longitudinal Bjorken expansion and a Hubble-like temperature cooling scenario on a $1+1$ dimensional nonlinear model of the diffusive dynamics of fluctuations in the net-baryon density. The equilibrium behavior of the fluctuations is fully encoded in the temperature dependence of the susceptibilities on the crossover side both in the vicinity of the assumed location of the critical point and at vanishing baryochemical potential in line with lattice quantum chromodynamics calculations. We demonstrate the great sensitivity of the fluctuation observables on the dynamics, in particular on the diffusion length and the freeze-out conditions. While the critical signals are visible and the critical region is broadened by the expansion, a too small diffusion length can strongly reduce the amplitude of the signals. We propose to search for significant anticorrelations of baryons at intermediate rapidity experimentally and to map out the rapidity dependence of the fourth-order cumulant, which, in the presence of a critical point (and only in its presence), has a pronounced minimum at intermediate rapidities.

Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of active research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model describing the evolution of water waves with higher-order temporal dispersion by characterizing the dynamics of lump and soliton waves on different spatially-varying backgrounds. Particularly, we construct some explicit lump wave and kink-soliton solutions for the considered model through its trilinear and bilinear equations with appropriate forms of the polynomial and exponential type initial seed solutions, respectively. Additionally, we obtain hyperbolic and periodic waves through bilinear Bäcklund transformation. We explore their propagation and transformation/modulation dynamics due to different spatial backgrounds through categorical analysis and clear graphical demonstrations for a complete understanding of the resulting solutions. Our analysis shows that the lump solution results into a simultaneous existence of well-localized spike and declining (coupled bright-dark wave) structures on a constant background, while the soliton solution exhibits kink and anti-kink wave patterns along different spatio-temporal domains with controllable properties. When the arbitrary spatial background is incorporated appropriately, we can witness the manifestation of soliton into manipulated periodic and interacting dynamical structures. On the other hand, the lump wave results into the coexistence, interacting wave and breather formation due to periodic and localized type arbitrary spatial backgrounds. The present results will be an important addition to the context of engineering nonlinear waves with non-vanishing controllable backgrounds in higher-dimensional models. Further, the present study can be extended to investigate several other nonlinear systems to understand the physical insights of the variable background in their dynamics.

Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple soliton solutions and a class of lump solutions

PurposeThis paper aims to propose a new (3+1)-dimensional integrable Hirota bilinear equation characterized by five linear partial derivatives and three nonlinear partial derivatives.Design/methodology/approachThe authors formally use the simplified Hirota's method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.FindingsThe Painlevé analysis shows that the compatibility condition for integrability does not die away at the highest resonance level, but integrability characteristics is justified through the Lax sense.Research limitations/implicationsMultiple-soliton solutions are explored using the Hirota's bilinear method. The authors also furnish a class of lump solutions using distinct values of the parameters via the positive quadratic function method.Practical implicationsThe authors also retrieve a bunch of other solutions of distinct structures such as solitonic, periodic solutions and ratio of trigonometric functions solutions.Social implicationsThis work formally furnishes algorithms for extending integrable equations and for the determination of lump solutions.Originality/valueTo the best of the authors’ knowledge, this paper introduces an original work with newly developed Lax-integrable equation and shows new useful findings.

Enabling in-time prognostics with surrogate modeling through physics-enhanced Dynamic Mode Decomposition method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the Prognostics and Health Management domain, where farahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. A potential solution was found by implementing Koopman theory, which considers the dynamics of nonlinear systems. Koopman theory provides a mechanism to trade-off low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the ProgPy python packages.

Degeneration of N-soliton solutions for a ($$3+1$$)-dimensional nonlinear model in shallow water waves

Degeneration of N-soliton solutions for a ($$3+1$$)-dimensional nonlinear model in shallow water waves

Sound synthesis of a 3D nonlinear string using a covariant Lie group integrator of a geometrically exact beam model

We present a three dimensional nonlinear string model based on a geometrically exact beam. The beam model is obtained by applying a variational principle using a covariant Lagrangian formulation; in particular, the equations of motion and the boundary conditions are treated in an unified manner. Following an analogous discrete variational principle, a Lie group variational integrator is given. The energy and momentum conservation properties of the integrator are discussed and illustrated. This geometrically exact beam serves as a basis to formulate a prestressed damped string model with coupled non trivial boundary conditions. Simulation results are discussed and validated against analytical solutions obtained in the context of a small displacement hypothesis.

Recurrent neural networks enable design of multifunctional synthetic human gut microbiome dynamics.

Predicting the dynamics and functions of microbiomes constructed from the bottom-up is a key challenge in exploiting them to our benefit. Current models based on ecological theory fail to capture complex community behaviors due to higher order interactions, do not scale well with increasing complexity and in considering multiple functions. We develop and apply a long short-term memory (LSTM) framework to advance our understanding of community assembly and health-relevant metabolite production using a synthetic human gut community. A mainstay of recurrent neural networks, the LSTM learns a high dimensional data-driven non-linear dynamical system model. We show that the LSTM model can outperform the widely used generalized Lotka-Volterra model based on ecological theory. We build methods to decipher microbe-microbe and microbe-metabolite interactions from an otherwise black-box model. These methods highlight that Actinobacteria, Firmicutes and Proteobacteria are significant drivers of metabolite production whereas Bacteroides shape community dynamics. We use the LSTM model to navigate a large multidimensional functional landscape to design communities with unique health-relevant metabolite profiles and temporal behaviors. In sum, the accuracy of the LSTM model can be exploited for experimental planning and to guide the design of synthetic microbiomes with target dynamic functions.

Formula omitted]-lump solution, soliton solution and rational solution to a (3+1)-dimensional nonlinear model

In the previous study, the one-lump solution is given to the dimensionally reduced forms of a (3+1)-dimensional nonlinear model via the positive quadratic function method. The main work of this paper is to construct the M-lump solution and the Wronskian solution to this (3+1)-dimensional nonlinear model. Firstly, the M-lump solution is constructed by using the long wave limit method. As an example, the three-dimensional plots of one-, two- and three-lump solutions and the corresponding density plots have been shown through selecting appropriate parameters. What is more, their motion process is analyzed systematically. Secondly, a sufficient condition of Wronskian solution is given by using the properties of determinant and Plücker relation. Based on the Wronskian form, we obtain the soliton solution and the rational solution by selecting the elements in the determinant which satisfy the linear partial differential systems. Finally, several specific examples are presented.

On some new analytical solutions to the (2+1)-dimensional nonlinear electrical transmission line model

In the present paper, from the field of communications in physics and engineering, we select the (2+1)-dimensional nonlinear electrical transmission line equation to be studied. The model under study is one of the models that has important applications in the field of physics and telecommunications engineering. We acquire the soliton solutions by using two simple methods. We present some figures in two and three dimensions to show that these solutions actually have the properties of soliton waves.

Self-similar transformation and excitation of rogue waves for (2+1)-dimensional Zakharov equation

The search for the excitation of two-dimensional rogue wave in a (2+1)-dimensional nonlinear evolution model is a research hotspot. In this paper, the self-similar transformation of the (2+1)-dimensional Zakharov equation is established, and this equation is transformed into the (1+1)-dimensional nonlinear Schrödinger equation. Based on the similarity transformation and the rational formal solution of the (1+1)-dimensional nonlinear Schrödinger equation, the rogue wave excitation of the (2+1)-dimensional Zakharov equation is obtained by selecting appropriate parameters. We can see that the shape and amplitude of the rogue waves can be effectively controlled. Finally, the propagation characteristics of line rogue waves are diagrammed visually. We also find that the line-type characteristics of two-dimensional rogue wave are present in the <i>x-y</i> plane when the parameter <inline-formula><tex-math id="M5">\begin{document}$ \gamma = 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M5.png"/></alternatives></inline-formula>. The line rogue wave is converted into discrete localized rogue wave in the <i>x-y</i> plane when the parameter <inline-formula><tex-math id="M6">\begin{document}$ \gamma \ne 1 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="8-20211181_M6.png"/></alternatives></inline-formula>. The spatial localized rogue waves with short-life can be obtained in the required <i>x-y</i> plane region. This is similar to the Peregrine soliton (PS) first discovered by Peregrine in the (1+1)-dimensional NLS equation, which is the limit case of the “Kuznetsov-Ma soliton” (KMS) or “Akhmediev breather” (AB). The proposed approach to constructing the line rogue waves of the (2+1) dimensional Zakharov equation can serve as a potential physical mechanism to excite two-dimensional rogue waves, and can be extended to other (2+1)-dimensional nonlinear systems.

On soliton solutions of fractional-order nonlinear model appears in physical sciences

<abstract><p>In wave theory, the higher dimensional non-linear models are very important to define the physical phenomena of waves. Herein study we have built the various solitons solutions of (4+1)-dimensional fractional-order Fokas equation by using two analytical techniques that is, the Sardar-subequation method and new extended hyperbolic function method. Different types of novel solitons are attained such as, singular soliton, bright soliton, dark soliton, and periodic soliton. To understand the physical behavior, we have plotted 2D and 3D graphs of some selected solutions. From results we concluded that the proposed methods are straightforward, simple, and efficient. Moreover, this paper offers a hint, how we can convert the fractional-order PDE into an ODE to acquire the exact solutions. Also, the proposed methods and results can be help to examine the advance fractional-order models which seem in optics, hydrodynamics, plasma and wave theory etc.</p></abstract>

Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of water waves and construct nonlinear wave solutions on spatio-temporally controllable backgrounds for the first time by using a simple mathematical tool auto-Bäcklund transformation. Mainly, we unravel physically interesting features to control and manipulate the dynamics of nonlinear waves through the background. Adapting an exponential function and general polynomial of degree two as initial seed solutions, we construct single kink-soliton and rogue wave, respectively. We choose arbitrary periodic, localized and combined wave backgrounds by incorporating Jacobi elliptic functions and investigate the modulation of these two nonlinear waves with a clear analysis and graphical demonstrations. The solutions derived in this work give us sufficient freedom to generate exotic nonlinear coherent structures on variable backgrounds and open up an interesting direction to explore the dynamics of various other nonlinear waves propagating through inhomogeneous media.

Scale symmetry breaking, quantum anomalous energy and proton mass decomposition

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales. We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition. We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks. We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.

Stiefel Liquids: Possible Non-Lagrangian Quantum Criticality from Intertwined Orders

We propose a new type of quantum liquids, dubbed Stiefel liquids, based on $2+1$ dimensional nonlinear sigma models on target space $SO(N)/SO(4)$, supplemented with Wess-Zumino-Witten terms. We argue that the Stiefel liquids form a class of critical quantum liquids with extraordinary properties, such as large emergent symmetries, a cascade structure, and nontrivial quantum anomalies. We show that the well known deconfined quantum critical point and $U(1)$ Dirac spin liquid are unified as two special examples of Stiefel liquids, with $N=5$ and $N=6$, respectively. Furthermore, we conjecture that Stiefel liquids with $N>6$ are non-Lagrangian, in the sense that under renormalization group they flow to infrared (conformally invariant) fixed points that cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of (conventional or parton-like) mean-field construction also means that, within the traditional approaches, it will be difficult to decide whether a non-Lagrangian state can actually emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.

Regarding New Traveling Wave Solutions for the Mathematical Model Arising in Telecommunications

This research paper focuses on the application of the tanh function method to find the soliton solutions of the (2+1)-dimensional nonlinear electrical transmission line model. Materials used to form a transmitting line are very important to transmit electric charge. In this sense, we find some new voltage behaviors such as dark, trigonometric, and complex function solutions. Choosing some suitable values of parameters, we present some various surfaces of results obtained in this paper. These results play an important role in telecommunications lines used to stand for wave propagations.

APPLICATION OF HOMOTOPY PERTURBATION METHOD TO THE MATHEMATICAL MODELLING OF TEMPERATURE RISE DURING MICROWAVE HYPERTHERMIA

We study a one dimensional non-linear model of multi-layered human skin exposed to microwave heating during cancer therapy. The model is analyzed using homotopy perturbation method and the fact that there are variations in specific heat, thermal conductivity and blood perfusion from one individual to another were considered. The purpose of this study was to investigate the effect of variable blood perfusion, microwave heating and thermal conductivity on the temperature field during microwave hyperthermia. By varying the parameters, we were able to determine maximum rise of temperature as an individual undergoes cancer therapy. The results were presented in graphs and it was discovered that the temperature of the tumor increases with increase in the microwave heating index while the blood perfusion remain constant.

Finite element analysis of square concrete columns strengthened with carbon fiber composites in different configurations

This paper offers the findings of numerical study carried out to evaluate the behavior of low strength concrete columns in square section strengthen by Carbon Fiber Reinforced Polymer (CFRP) composites and subjected to axial compression load. In this study, a three dimensional non-linear finite element formulation model has been presented using ANSYS-16.1 (software computer program) to analyse low strength concrete columns in square section strengthen by CFRP composites in different configurations, to evaluate the improvement in the ultimate load capacities of columns as a result of CFRP confinement, and to study the impact of the most important parameters such as: compressive strength of concrete, thickness of the CFRP layers jacket/strips and the presence of steel reinforcement on the performance of th modelled columns subjected to compression load. A comparison has been made between the results obtained from the Finite Element Analysis (FEA) and experimental data. The results of the numerical FEA study showed that, external strengthening with CFRP composites are very effective in upgrading the ultimate load of square concrete columns. In addition, the findings revealed good agreement between the ANSYS and the experimental test results. The results obtained from the parametric study revealed that when the CFRP layers increased from 2 to 3 layers and from 2 to 4 layers the ultimate loads of the columns increased about (2%-10%) and (7%-15%) respectively. While the compressive strength showed significant effect on the upgrade of the ultimate load, when increase the compressive strength to 42MPa and to 60 MPa, the ultimate load increased to about 220% and to about 300% respectively. The presence of steel reinforcing did not show reasonable effect on the ultimate load.

Quantum anomalous energy effects on the nucleon mass

Apart from the quark and gluon kinetic and potential energies, the nucleon mass includes a novel energy of pure quantum origin resulting from anomalous breaking of scale symmetry. We demonstrate the effects of this quantum anomalous energy (QAE) in QED, as well as in a toy 1 + 1 dimensional non-linear sigma model where it contributes non-perturbatively, in a way resembling the Higgs mechanism for the masses of matter particles in electro-weak theory. The QAE contribution to the nucleon mass can be explained using a similar mechanism, in terms of a dynamical response of the gluonic scalar field through Higgs-like couplings between the nucleon and scalar resonances. In addition, the QAE sets the scale for other energies in the nucleon through a relativistic virial theorem, and contributes a negative pressure to confine the colored quarks.

A Framework with reduced computational burden for Seismic Fragility Assessment of Reinforced Concrete Buildings in High-Intensity Seismic Zones

The current research is targeted to develop the analytical fragility relationships of reinforced concrete (RC) buildings in high-intensity seismic zones by considering the effects of higher structural modes to reduce the computational effort. A new framework is presented in the study to assess the vulnerability in terms of the fragility relationships that can consider the modal response of individual modes in a building structure. The developed methodology considers the uncoupled modes of a structure employing a nonlinear single degree of freedom structures and defines distinct limit states for each mode separately. By using the presented methodology, the response of higher modes can be incorporated in the fragility assessment. For elucidation, a two-story reinforced concrete (RC) school building structure is selected from seismic zone 4 of Pakistan. In the first place, its vulnerability is assessed by developing fragility relationships using dynamic response history analysis of full three Dimensional nonlinear analytical models, subsequently, the fragility relationships are developed using the presented methodology by considering the first two modes of the structure. Afterward, a comparison has been made between the developed fragility curves from both of the methodologies. The results prove the effectiveness, swiftness, and the simplicity of the established methodology for carrying out the vulnerability assessments without compromising any accuracy. The developed framework reduces the computational time of one calculation cycle from 72 h for conventional methods to merely 4 h using a regular computer.

A new three dimensional dissipative Boussinesq equation for Rossby waves and its multiple soliton solutions

A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a three dimensional dissipative Boussinesq equation by the reduced perturbation method, i.e.utt+e1uxx+e2(u2)xx+e3utxy+e4uxxxx+e5uxxyy=0. It is emphasized that the new equation is different from the existing Boussinesq equations, which describe the three dimensional nonlinear Rossby waves in the atmosphere. Moreover, we explore the dispersion relation of the linear wave through the new equation. Using the travelling wave method and simplest equation method, the general solution and soliton solutions of the equation are obtained successfully respectively. Finally, the formation mechanism of Rossby waves is discussed by multiple soliton solutions.