Residual symmetry, interaction solutions, and conservation laws of the(2+1)-dimensional dispersive long-wave system

We explore the （2＋l）-dimensional dispersive long-wave （DLW） system. From the standard truncated Painleve expansion, the Baicklund transformation （BT） and residual symmetries of this system are derived. The introduction to an appropriate auxiliary dependent variable successfully localizes the residual symmetries to Lie point symmetries. In particular, it is verified that the （2＋l）-dimensional DLW system is consistent Riccati expansion （CRE） solvable. If the special form of （CRE）-consistent tanh-function expansion （CTE） is taken, the soliton-cnoidal wave solutions and corresponding images can be explicitly given. Furthermore, the conservation laws of the DLW system are investigated with symmetries and Ibragimov theorem.

Elastoplastic pipe-soil interaction analyses of partially-supported jointed water mains

Water distribution networks are essential components of water supply systems. The combination of pipe structural deterioration and mechanics leads to the failure of pipelines. A physical model for estimating the pipe failure must include both the pipe deterioration model and mechanics model. Winkler pipe-soil interaction (WPSI), an analytical mechanics model developed by Rajani and Tesfamariam (2004), takes external and internal loads, temperature changes, loss of bedding support, and the elastoplastic effect of soil into consideration. Based on the WPSI model, a method to evaluate the elastic and plastic areas was proposed in the present study. An FEM model based on pipe-soil interaction (PSI) element was used to verify the analytical model. Sensitivity analyses indicate that the soft soil, long pipe and high temperature induced the axial plastic deformation more likely, which, however, may not occur in normal scenarios. The soft soil, pipes in small diameters, long unsupported bedding are prone to form flexural plastic area. The results show that the pipes subjected to the same loads have smaller stresses in the elastoplastic analysis than elastic analysis. The difference, however, is slight.

Modeling pipe-soil interaction under vertical downward relative offset using B-spline material point method

To analyze the pipeline response under permanent ground deformation,the evolution of resistance acting on the pipe during the vertical downward offset is an essential ingredient.However,the efficient simulation of pipe penetration into soil is challenging for the conventional finite element(FE)method due to the large deformation of the surrounding soils.In this study,the B-spline material point method(MPM)is employed to investigate the pipe-soil interaction during the downward movement of rigid pipes buried in medium and dense sand.To describe the density-and stress-dependent behaviors of sand,the J2-deformation type model with state-dependent dilatancy is adopted.The effectiveness of the model is demonstrated by element tests and biaxial compression tests.Afterwards,the pipe penetration process is simulated,and the numerical outcomes are compared with the physical model tests.The effects of pipe size and burial depth are investigated with an emphasis on the mobilization of the soil resistance and the failure mechanisms.The simulation results indicate that the bearing capacity formulas given in the guidelines can provide essentially reasonable estimates for the ultimate force acting on buried pipes,and the recommended value of yield displacement may be underestimated to a certain extent.

Power Law Nature in Electron Solid Interaction

Monte Carlo simulation of paths of a large number of impinging electrons in a multi-layered solid allows defining area of spreading electrons (A) to capture overall behavior of the solid. This parameter “A” follows power law with electron energy. Furthermore, change in critical energies, which are minimum energies loses corresponding to various electrons, as a function of variation in lateral distance also follows power law nature. This power law behavior could be an indicator of how strong self-organization a solid has which may be used in monitoring efficiency of device fabrication.

Analysis of Electrical Dipoles Interaction Forces as a Function of the Distance and of the Form of Electrical Force Law

Here, we initially introduced and demonstrated two principles: orientation OR principle and attraction AT principle of electrical dipoles. The OR principle stipulates that any two electrical dipoles P1A, P1B, from two bodies A and B, at any distance in the free state each, will be reciprocally oriented parallel and in the same sense if the electrical interaction forces F between them are of decreasing type with distance r. If the electrical interaction forces F are of increasing type with distance, the two dipoles will be reciprocally oriented parallel but on the opposite sense. The AT principle stipulate that any two electrical dipoles P1A, P1B, at any distance in the free state each, will present always a reciprocal force of attraction FD in both cases of orientation accordingly to OR principle in case of any type of electrical force F decreasing or increasing with distance. These findings may complete our previous work where we found that FD force, between two electrical dipoles P1A, P1B considered at atomic and nuclear level, is in fact the actual gravitation Newton force FN. The paper must be considered together with this work for more consistency.

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

We applied n-variable conserving nonlinear differential equations (n-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... n-variable conserving nonlinear interactions (n-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as a standard rhythm of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem.

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.

The Protection of the Right to Dignity in the Connection and Interaction between the Constitution and Civil Law

In the report of 19;National Congress of the Communist Party of China,General Secretary Xi Jinping said that China seeks to"accelerate development of the crime prevention and control system,combat and punish in accordance with law all illegal and criminal activities such as pornography,gambling,drug abuse,gang violence,kidnapping,and fraud,and protect people’s personal rights,property rights,and right

A NOTE ON THE INTERACTIONS OF ELEMENTARY WAVES FOR THE AR TRAFFIC FLOW MODEL WITHOUT VACUUM

In this note, we consider the interactions of elementary waves for the traffic flow model proposed by Aw and Rascle when the vacuum is not involved. The solutions are obtained constructively and globally when the initial data consist of three pieces of constant states. Furthermore, it can be found that the Riemann solutions are stable with respect to such small perturbations of the initial data in this particular situation by investigating the limits of the solutions as the perturbed parameter ε goes to zero.

Fluid-Structure Interaction Modeling of the Living Artery: Based on the Zero-Pressure Status and the Anisotropic Hyperelastic Constitutive Model

Vascular diseases such as aneurysm,hemadostenosis,aortic dissection are the primary causes of people’s death around world.As a result,it is significant to improve our knowledge about them,which can help to treat the disease.Measuring the hemodynamic factor like the blood pressure,the wall shear stress(WSS)and the oscillatory shear index(OSI)is,however,still beyond the capabilities of in-vivo measurement techniques.So the use of mathematical models and numerical simulations for the studies of the blood flow in arteries and,in general,of the cardiovascular system,both in physiological and pathological conditions,has received an increasing attention in the biomedical community during the last two decades.Indeed,such studies aims at enhancing the current knowledge of the physiology of the cardiovascular system,as well as providing reliable tools for the medical doctors to predict the natural course of pathologies and,possibly,the occurrence of cardiovascular accidents.The computational vascular fluid-structure interaction(FSI)methodology is a numerical simulation method which is used to explain the hemodynamic factors.The WSS on the luminal wall and the mechanical stress in the vascular wall are directly related to the location of the lesion,and the blood flow strongly interacts with the vascular wall motion.The arterial wall continually adapts to the charge of its mechanical environment(due to,for example,growth,atrophy,remodelling,repair,ageing,and disease)and consequently undergoes several irreversible processes.Primary acute mechanisms of vascularFSI numerical simulation seem to be associated with(1)the arterial histology and the patient-specific complex geometry,(2)the typical mechanical properties of the layer,(3)properties of the blood is assumed as Newtonian fluid or non-Newtonian fluid based on the scale ofthe diameter of a vessel,(4)residual stress in the zero-pressure configuration.The arterial system naturally function under permanent physiological loading conditions.Fung defined the residual stress and measured the opening angle which varies greatly along the aortic tree.Consequently,most of these systems never experience a stress-free state in their’service life’,so a stress and strain fields are present in any in vivo obtained patientspecific cardiovascular geometry.The residual stress always be ignored in FSI simulation or be assumed to equal zero,and the vivo patient-specific artery geometry is assumed as zero-pressure configuration.To define the in vivo stress state of artery,an inverse problem needs to be solved:the undeformed shape of a body or its stress state in its deformed state needs to be determined given the deformed configuration and the loads causing this deformation.The modular inverse elastostatics method is used to resolve the pressure-induced stress state for in vivo imaging based on cardiovascular modeling proposed by Peirlinck.Here,we build a living vessel FSI model based on 4 key factors.In order to get the universal simulation results,we focus on idealized geometries of the vessel that represent healthy(physiological)conditions of the cerebral vasculature.Blood can be assumed as the Newtonian fluid at this scale.The anisotropic hyperelastic constitutive law(Gasser-Holzapfel-Ogden)is used in zero-pressure configuration.Afterwards,we propose the material parameters for the different constitutive models and the computational configurations.We demonstrate the importance of introducing the residual stress into vascular blood flow modeling by performing a comparing zero-pressure configuration and no-resistance configuration.We get the conclusion that the zero-pressure status model has smaller displacement and larger stress distribution compared with no-resistance stress model.Hence,the methodology presented here will be particularly useful to study the mechanobiological processes in the healthy and diseased vascular wall.

On the electron sheath theory and its applications in plasma–surface interactions

In this work,an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on their implications for plasma–surface interactions.A fluid model is proposed considering the electron presheath structure,avoiding the singularity in electron sheath Child–Langmuir law which overestimates the sheath potential.Subsequently,a kinetic model of electron sheath is established,showing considerably different sheath proflles in respect to the fluid model due to non-Maxwellian electron velocity distribution function and flnite ion temperature.The kinetic model is then further generalized and involves a more realistic truncated ion velocity distribution function.It is demonstrated that such a distribution function yields a super-thermal electron sheath whose entering velocity at the sheath edge is greater than the Bohm criterion prediction.Furthermore,an attempt is made to describe the electron presheath–sheath coupling within the kinetic framework,showing a necessary compromise between a realistic sheath entrance and the inclusion of kinetic effects.Finally,the secondary electron emissions induced by sheath-accelerated plasma electrons in an electron sheath are analysed and the influence of backscattering is discussed.

Elementary Wave Interactions for the Simplified Combustion Model in Magnetogasdynamics

We investigate the elementary wave interactions for the simplified combustion model in magnetogasdynamics. Under the modified entropy conditions, we construct the unique solution and observe some interesting phenomena;such as, the combustion wave may be extinguished by the contact discontinuity or the shock wave. Especially, the transition between the detonation wave and the deflagration wave is also captured.

Wave Interactions of the Aw-Rascle Model for Generalized Chaplygin Gas

In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.

Numerical Experiment for Dipole-Dipole Interaction in Electro-Magnetism with Help of a Regular Tetrahedron

Aim of this work is to try to explain, on a Rational basis, some equations of Electro-Magnetism, which are based on Experimental data. Any Electric Field can produce a Field of many small Electric Dipoles, continuously distributed in space. In a region, where the Electric Field is constant, in direction and magnitude, all the small Dipoles are parallel to the Electric Field, and are represented by a single, long, parallel to them, fixed in space, Electric Dipole, which is here called Compass. An Alternating current, in a straight Conductor, is studied, by a simple, short computer program, for step-by-step nonlinear dynamic analysis. It is found that, only an Alternating current, not a direct current, can produce an Electric Dipole, in a straight Conductor. The two above Dipoles (Compass-Conductor) are assumed with equal lengths ℓ, lying on two skew lines, perpendicular to each other, at a distance ℓ√2, thus forming, by their four ends, a Regular Tetrahedron, with side length ℓ. Repulsion, between Like Charges, obeys the simple Coulomb Electro-Static law. Whereas Interaction (Attraction or Repulsion), between Unlike Charges, obeys a more accurate Lennard-Jones law. The analysis of Dipole-Dipole (Compass-Conductor) Interaction is performed by hand calculator. The only out-of-balance forces, in the regular Tetrahedron, acting on the Rigid Conductor, are the so-called magnetic forces. Their direction is found, in a simple Rational way, with help of Regular Tetrahedron, without recoursing to a “right-hand-rule”. The proposed model is applied to 1) The force acting on an Electric Charge moving in a magnetic field. 2) The force acting on a Current carrying straight Conductor, due to a magnetic field. 3) The magnetic fields created around a Current carrying straight Conductor. In these applications, proposed model gives reasonable results. Particularly, in third application, results, obtained by proposed model, are found in satisfactory approximation with corresponding ones, obtained by an empirical formula, based on relevant Experimental observations of H.-C. Oersted and A.-M. Ampère. So, the reliability of proposed model is checked. Position and direction of magnetic field vector coincide with those of a corresponding fixed Compass of a constant Electric Field. Main point of present work is that, without introducing the concept of a magnetic field vector, by combining field of dipoles, produced by an electric field, with dipole of an alternating current carrying conductor, the magnetic forces can be determined.

Wave Interactions for the Suliciu Relaxation System

In this paper, we investigate the elementary wave interactions for the Suliciu relaxation system and construct uniquely the solution by the characteristic analysis method in the phase plane. We find that the elementary wave interactions have a much simpler structure for the Temple class than the general systems of conservation laws. It is observed that the Riemann solutions of the Suliciu relaxation system are stable under the small perturbation on the Riemann initial data.

Transcription's bubble under the influence of long-range interactions and helicoidal coupling

The influence of power-low long-range interactions （LRI） and helicoidal coupling （HC） on the properties of localized solitons in a DNA molecule when a ribonucleic acid polymerase （RNAP） binds to it at the physiological temperature is analytically and numerically investigated in this paper. We have made an analogy with the Heisenberg model Hamiltonian of an anisotropic spin ladder with ferromagnetic legs and anti-ferromagnetic rung coupling. When we limit ourselves to the second-order terms in the Taylor expansion, the DNA dynamics is found to be governed by a completely integrable nonlinear Schr？dinger （NLS） equation. In this case, results show that increasing the value of HC force or LRI parameter enhances the bubble height and reduces the number of base pairs which form the bubble. For the fourth-order terms in a Taylor expansion, results are closely resembling those of second-order terms, and are confirmed by numerical investigation. These results match with some experimental data and thus provide a better representation of the base pairs opening in DNA which is essential for the transcription process.

Conservation Laws of Physics in Dirac Vacuum and β-Decay of Nuclei

The laws of conservation of energy, linear momentum. and angular momentum of a system form a closed unit according to Noether's theorem. A generalization of these laws (including spin) for elementary par- ticles taking into account the states of negative energies of the Dirac vacuum is given. A new interpretation of the β-decay of nuclei without neutrinos. using interactions with Dirac's anti-world is discussed, which ex- plains all characteristics of the β-continuum. A quantum-electrodynamic theory of β-decay is presented in which Fermi's constant g of weak interactions is determined from first principles (without neutrinos). The lat- ter is an expression of e, h, c, m, M, and R, i.e., g is not an independent constant of physics nor is it necessa- ry to measure it.

A LIMIT THEOREM FOR INTERACTING MEASURE-VALUED BRANCHING PROCESSES

It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.

DECAY OF POSITIVE WAVES OF HYPERBOLIC BALANCE LAWS

Historically, decay rates have been used to provide quantitative and quali- tative information on the solutions to hyperbolic conservation laws. Quantitative results include the establishment of convergence rates for approximating procedures and numer- ical schemes. Qualitative results include the establishment of results on uniqueness and regularity as well as the ability to visualize the waves and their evolution in time. This work presents two decay estimates on the positive waves for systems of hyperbolic and gen- uinely nonlinear balance laws satisfying a dissipative mechanism. The result is obtained by employing the continuity of Glimm-type functionals and the method of generalized characteristics [7, 17, 241.

Features of Malus Law in the Region of X-Ray Radiation

The light propagation through system a polarizer-analyzer is investigated on the basis of quantum conceptions about the nature of light. It is shown, that Malus law based on principles of classical electrodynamics not completely takes into account all effects which can occur at the light propagation through system a polarizer-analyzer. The phenomenon of possible change of frequency of light in particular drops out, for example in the region of X-ray radiation. The deduction of Malus law based on quantum principles is given. For comparison the differential effective section of interaction of a photon and electron with take into account of rotation of a plane of polarization of a photon in Compton’s effect is found.