**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**197

# Search results for: relativistic mechanics

##### 197 Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

**Authors:**
H. Loumi-Fergane,
A. Belaidi

**Abstract:**

The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in q^{i}, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

**Keywords:**
Field theories,
relativistic mechanics,
Lagrangian formalism,
multisymplectic geometry,
symmetries,
Noether theorem,
conservation laws.

##### 196 De Broglie Wavelength Defined by the Rest Energy E0 and Its Velocity

**Authors:**
K. Orozović,
B. Balon

**Abstract:**

In this paper, we take a different approach to de Broglie wavelength, as we relate it to relativistic physics. The quantum energy of the photon radiated by a body with de Broglie wavelength, as it moves with velocity v, can be defined within relativistic physics by rest energy E₀. In this way, we can show the connection between the quantum of radiation energy of the body and the rest of energy E₀ and thus combine what has been incompatible so far, namely relativistic and quantum physics. So, here we discuss the unification of relativistic and quantum physics by introducing the factor k that is analog to the Lorentz factor in Einstein's theory of relativity.

**Keywords:**
de Brogli wavelength,
relativistic physics,
rest energy,
quantum physics.

##### 195 Phenomenological and Theoretical Analysis of Relativistic Temperature Transformation and Relativistic Entropy

**Authors:**
Marko Popovic

**Abstract:**

**Keywords:**
STR,
relativistic temperature transformation,
Boyle'slaw,
equilibrium constant,
Gibbs energy.

##### 194 Propagation of Electron-Acoustic Solitary Waves in Weakly Relativistically Degenerate Fermi Plasma

**Authors:**
Swarniv Chandra,
Basudev Ghosh,
S. N. Paul

**Abstract:**

**Keywords:**
Relativistic Degeneracy,
Electron-Acoustic Waves,
Quantum Plasma,
KdV Equation.

##### 193 Axiomatic Systems as an Alternative to Teach Physics

**Authors:**
Liliana M. Marinelli,
Cristina T. Varanese

**Abstract:**

In the last few years, students from higher education have difficulties in grasping mathematical concepts which support physical matters, especially those in the first years of this education. Classical Physics teaching turns to be complex when students are not able to make use of mathematical tools which lead to the conceptual structure of Physics. When derivation and integration rules are not used or developed in parallel with other disciplines, the physical meaning that we attempt to convey turns to be complicated. Due to this fact, it could be of great use to see the Classical Mechanics from an axiomatic approach, where the correspondence rules give physical meaning, if we expect students to understand concepts clearly and accurately. Using the Minkowski point of view adapted to a two-dimensional space and time where vectors, matrices, and straight lines (worked from an affine space) give mathematical and physical rigorosity even when it is more abstract. An interesting option would be to develop the disciplinary contents from an axiomatic version which embraces the Classical Mechanics as a particular case of Relativistic Mechanics. The observation about the increase in the difficulties stated by students in the first years of education allows this idea to grow as a possible option to improve performance and understanding of the concepts of this subject.

**Keywords:**
Axiom,
classical physics,
physical concepts,
relativity.

##### 192 Propagation of Nonlinear Surface Waves in Relativistically Degenerate Quantum Plasma Half-Space

**Authors:**
Swarniv Chandra,
Parthasona Maji,
Basudev Ghosh

**Abstract:**

The nonlinear self-interaction of an electrostatic surface wave on a semibounded quantum plasma with relativistic degeneracy is investigated by using quantum hydrodynamic (QHD) model and the Poisson’s equation with appropriate boundary conditions. It is shown that a part of the second harmonic generated through self-interaction does not have a true surface wave character but propagates obliquely away from the plasma-vacuum interface into the bulk of plasma.

**Keywords:**
Harmonic Generation,
Quantum Plasma,
Quantum Hydrodynamic Model,
Relativistic Degeneracy,
Surface waves.

##### 191 Central Finite Volume Methods Applied in Relativistic Magnetohydrodynamics: Applications in Disks and Jets

**Authors:**
Raphael de Oliveira Garcia,
Samuel Rocha de Oliveira

**Abstract:**

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

**Keywords:**
Finite Volume Methods,
Central Schemes,
Fortran
90,
Relativistic Astrophysics,
Jet.

##### 190 A Unification and Relativistic Correction for Boltzmann’s Law

**Authors:**
Lloyd G. Allred

**Abstract:**

The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (*E=mc ^{2}*), then a relativistic correction is not required.

**Keywords:**
Cosmology,
EMP,
Euclidean,
plasma physics,
relativity.

##### 189 Shell Closures in Exotic Nuclei

**Authors:**
G. Saxena,
D. Singh,
M. Kaushik,

**Abstract:**

**Keywords:**
Relativistic Mean Field theory,
Magic Nucleus,
Si
isotopes,
Shell Closure.

##### 188 The Self-Energy of an Ellectron Bound in a Coulomb Field

**Authors:**
J. Zamastil,
V. Patkos

**Abstract:**

Recent progress in calculation of the one-loop selfenergy of the electron bound in the Coulomb field is summarized. The relativistic multipole expansion is introduced. This expansion is based on a single assumption: except for the part of the time component of the electron four-momentum corresponding to the electron rest mass, the exchange of four-momentum between the virtual electron and photon can be treated perturbatively. For non Sstates and normalized difference n3En −E1 of the S-states this itself yields very accurate results after taking the method to the third order. For the ground state the perturbation treatment of the electron virtual states with very high three-momentum is to be avoided. For these states one can always rearrange the pertinent expression in such a way that free-particle approximation is allowed. Combination of the relativistic multipole expansion and free-particle approximation yields very accurate result after taking the method to the ninth order. These results are in very good agreement with the previous results obtained by the partial wave expansion and definitely exclude the possibility that the uncertainity in determination of the proton radius comes from the uncertainity in the calculation of the one-loop selfenergy.

**Keywords:**
Hydrogen-like atoms,
self-energy.

##### 187 Continuum-Based Modelling Approaches for Cell Mechanics

**Authors:**
Yogesh D. Bansod,
Jiri Bursa

**Abstract:**

**Keywords:**
Cell mechanics,
computational models,
continuum
approach,
mechanical models.

##### 186 Combining Laws of Mechanics and Hydrostatics in Non-Inertial Reference Frames

**Authors:**
M. Blokh

**Abstract:**

**Keywords:**
Hydrodynamics,
mechanics,
non-inertial reference
frames,
teaching.

##### 185 Fatigue Failure of Structural Steel – Analysis Using Fracture Mechanics

**Abstract:**

**Keywords:**
fatigue,
fracture mechanics,
fatigue testing machine

##### 184 Quantum Ion Acoustic Solitary and Shock Waves in Dissipative Warm Plasma with Fermi Electron and Positron

**Authors:**
Hamid Reza Pakzad

**Abstract:**

**Keywords:**
Ion acoustic shock waves; Quantum plasmas

##### 183 2D Fracture Analysis of the First Compression Piston Ring

**Authors:**
I. Razmi,
N. Choupani

**Abstract:**

**Keywords:**
Compression piston ring,
Crack,
Fracture
mechanics,
SEM fractography.

##### 182 An Approximation Method for Three Quark Systems in the Hyper-Spherical Approach

**Authors:**
B. Rezaei,
G. R. Boroun,
M. Abdolmaleki

**Abstract:**

The bound state energy of three quark systems is studied in the framework of a non- relativistic spin independent phenomenological model. The hyper- spherical coordinates are considered for the solution this system. According to Jacobi coordinate, we determined the bound state energy for (uud) and (ddu) quark systems, as quarks are flavorless mass, and it is restrict that choice potential at low and high range in nucleon bag for a bound state.

**Keywords:**
Adiabatic expansion,
grand angular momentum,
binding energy,
perturbation,
baryons.

##### 181 The Applications of Quantum Mechanics Simulation for Solvent Selection in Chemicals Separation

**Authors:**
Attapong T.,
Hong-Ming Ku,
Nakarin M.,
Narin L.,
Alisa L,
Jirut W.

**Abstract:**

**Keywords:**
Extractive distillation,
Interaction force,
Quamtum mechanic,
Relative volatility,
Solvent extraction.

##### 180 Maximizer of the Posterior Marginal Estimate of Phase Unwrapping Based On Statistical Mechanics of the Q-Ising Model

**Authors:**
Yohei Saika,
Tatsuya Uezu

**Abstract:**

We constructed a method of phase unwrapping for a typical wave-front by utilizing the maximizer of the posterior marginal (MPM) estimate corresponding to equilibrium statistical mechanics of the three-state Ising model on a square lattice on the basis of an analogy between statistical mechanics and Bayesian inference. We investigated the static properties of an MPM estimate from a phase diagram using Monte Carlo simulation for a typical wave-front with synthetic aperture radar (SAR) interferometry. The simulations clarified that the surface-consistency conditions were useful for extending the phase where the MPM estimate was successful in phase unwrapping with a high degree of accuracy and that introducing prior information into the MPM estimate also made it possible to extend the phase under the constraint of the surface-consistency conditions with a high degree of accuracy. We also found that the MPM estimate could be used to reconstruct the original wave-fronts more smoothly, if we appropriately tuned hyper-parameters corresponding to temperature to utilize fluctuations around the MAP solution. Also, from the viewpoint of statistical mechanics of the Q-Ising model, we found that the MPM estimate was regarded as a method for searching the ground state by utilizing thermal fluctuations under the constraint of the surface-consistency condition.

**Keywords:**
Bayesian inference,
maximizer of the posterior
marginal estimate,
phase unwrapping,
Monte Carlo simulation,
statistical mechanics

##### 179 The Study on Mechanical Properties of Graphene Using Molecular Mechanics

**Authors:**
I-Ling Chang,
Jer-An Chen

**Abstract:**

**Keywords:**
Energy minimization,
fracture,
graphene,
molecular
mechanics.

##### 178 Process Analysis through Length Consistency

**Authors:**
James E. Ponder

**Abstract:**

The requirement for consistency in physics can sometimes offer a common ground between disciplines such that their fundamental equations share a common parameter set and mathematical method for equation extraction. The parameter set shared by Relativity and Quantum Wave Mechanics enables an analysis which will be seen to be very straightforward, primarily classical in nature using linear algebra concepts, yet deriving a theoretical estimate of the value of the Gravitational Constant along with dependencies never before known.

**Keywords:**
Gravitational Constant,
Physical Consistency,
Quantum Mechanics,
Relativity.

##### 177 Fracture Mechanics Modeling of a Shear-Cracked RC Beams Shear-Strengthened with FRP Sheets

**Authors:**
Shahriar Shahbazpanahi,
Alaleh Kamgar

**Abstract:**

So far, the conventional experimental and theoretical analysis in fracture mechanics have been applied to study concrete flexural- cracked beams, which are strengthened using fiber reinforced polymer (FRP) composite sheets. However, there is still little knowledge about the shear capacity of a side face FRP- strengthened shear-cracked beam. A numerical analysis is herein presented to model the fracture mechanics of a four-point RC beam, with two inclined initial notch on the supports, which is strengthened with side face FRP sheets. In the present study, the shear crack is forced to conduct by using an initial notch in supports. The ABAQUS software is used to model crack propagation by conventional cohesive elements. It is observed that the FRP sheets play important roles in preventing the propagation of shear cracks.

**Keywords:**
Crack,
FRP,
shear,
strengthening.

##### 176 Newtonian Mechanics Descriptions for General Relativity Experimental Tests, Dark Matter and Dark Energy

**Authors:**
Jing-Gang Xie

**Abstract:**

As the continuation to the previous studies of gravitational frequency shift, gravitational time dilation, gravitational light bending, gravitational waves, dark matter, and dark energy are explained in the context of Newtonian mechanics. The photon is treated as the particle with mass of hν/C^{2} under the gravitational field of much larger mass of M. Hence the quantum mechanics theory could be applied to gravitational field on cosmology scale. The obtained results are the same as those obtained by general relativity considering weak gravitational field approximation; however, the results are different when the gravitational field is substantially strong.

**Keywords:**
Gravitational time dilation,
gravitational light bending,
gravitational waves,
dark matter,
dark energy,
General Relativity,
gravitational frequency shift.

##### 175 Study of Crashworthiness Behavior of Thin-Walled Tube under Axial Loading by Using Computational Mechanics

**Authors:**
M. Kamal M. Shah,
Noorhifiantylaily Ahmad,
O. Irma Wani,
J. Sahari

**Abstract:**

This paper presents the computationally mechanics analysis of energy absorption for cylindrical and square thin wall tubed structure by using ABAQUS/explicit. The crashworthiness behavior of AISI 1020 mild steel thin-walled tube under axial loading has been studied. The influence effects of different model’s cross-section, as well as model length on the crashworthiness behavior of thin-walled tube, are investigated. The model was placed on loading platform under axial loading with impact velocity of 5 m/s to obtain the deformation results of each model under quasi-static loading. The results showed that model undergoes different deformation mode exhibits different energy absorption performance.

**Keywords:**
Axial loading,
energy absorption performance,
computational mechanics,
crashworthiness behavior,
deformation mode,
thin-walled tubes.

##### 174 Mixed-Mode Study of Rock Fracture Mechanics by using the Modified Arcan Specimen Test

**Authors:**
R. Hasanpour,
N. Choupani

**Abstract:**

**Keywords:**
Rock Fracture Mechanics,
Mixed-mode Loading,
Finite Element Analysis,
Arcan Test specimen.

##### 173 Three-Dimensional State with Doublet Mechanics

**Authors:**
Hilal Koç,
Ekrem Tüfekci

**Abstract:**

In this study, it is aimed to obtain general stress expressions for the examination of mechanical behaviors of planar straight axis nano rods by using doublet mechanics. The superiority of this method over other scale dependent methods is that it is directly related to the structure of nanomaterial and it models solid structure with points at finite distances between them. In other words, value of small scale effect is known exactly. To the best of authors’ knowledge, after micro modulus matrix is obtained by using Generalized Hooke’s Law and the essential transformation matrix expressing relationships between macro and micro stress and strain matrix, the stress equations that include the effect of axial extension are acquired for the three-dimensional state for the first time in the literature. In plane and out of plane static and dynamic behaviors can be studied using analytical and/or numerical approaches without any restrictions. Since the value of the small scale size parameter is precisely known in the theory used, it is thought that the results to be obtained will be more accurate than other scale size theories.

**Keywords:**
axial extension,
doublet mechanics,
granular material,
three-dimensional state

##### 172 Calculation of Wave Function at the Origin (WFO) for the Ground State of Doubly Heavy Mesons Based On the Variational Method

**Authors:**
Maryam Momeni Feili,
Mahvash Zandy Navgaran

**Abstract:**

The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.

**Keywords:**
Wave function at the origin,
heavy mesons,
bound states,
variational method,
non-relativistic quark model,
potential model,
trial wave function.

##### 171 A Self-Consistent Scheme for Elastic-Plastic Asperity Contact

**Authors:**
Xu Jianguo

**Abstract:**

In this paper, a generalized self-consistent scheme, or “three phase model", is used to set up a micro-mechanics model for rough surface contact with randomly distributed asperities. The dimensionless average real pressure p is obtained as function of the ratio of the real contact area to the apparent contact area, 0 A / A r . Both elastic and plastic materials are considered, and the influence of the plasticity of material on p is discussed. Both two-dimensional and three-dimensional rough surface contact problems are considered.

**Keywords:**
Contact mechanics,
plastic deformation,
self-consistent scheme.

##### 170 Nonplanar Ion-acoustic Waves in a Relativistically Degenerate Quantum Plasma

**Authors:**
Swarniv Chandra,
Sibarjun Das,
Agniv Chandra,
Basudev Ghosh,
Apratim Jash

**Abstract:**

**Keywords:**
Kadomtsev-Petviashvili equation,
Ion-acoustic
Waves,
Relativistic Degeneracy,
Quantum Plasma,
Quantum
Hydrodynamic Model.

##### 169 Effect of Miniature Cracks on the Fracture Strength and Strain of Tensile Armour Wires

**Authors:**
Kazeem K. Adewole,
Steve J. Bull

**Abstract:**

**Keywords:**
Cracks,
Finite Element Simulations,
Fracture
Mechanics,
Shear Fracture Model,
Tensile Armour Wire

##### 168 The Application of FSI Techniques in Modeling of Realist Pulmonary Systems

**Authors:**
Abdurrahim Bolukbasi,
Hassan Athari,
Dogan Ciloglu

**Abstract:**

The modeling lung respiratory system that has complex anatomy and biophysics presents several challenges including tissue-driven flow patterns and wall motion. Also, the pulmonary lung system because of that they stretch and recoil with each breath, has not static walls and structures. The direct relationship between air flow and tissue motion in the lung structures naturally prefers an FSI simulation technique. Therefore, in order to toward the realistic simulation of pulmonary breathing mechanics the development of a coupled FSI computational model is an important step. A simple but physiologically relevant three-dimensional deep long geometry is designed and fluid-structure interaction (FSI) coupling technique is utilized for simulating the deformation of the lung parenchyma tissue that produces airflow fields. The real understanding of respiratory tissue system as a complex phenomenon have been investigated with respect to respiratory patterns, fluid dynamics and tissue viscoelasticity and tidal breathing period.

**Keywords:**
Lung deformation and mechanics,
tissue mechanics,
viscoelasticity,
fluid-structure interactions,
ANSYS.