scholarly journals Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Kai Ma
Keyword(s):  
Fluid Dynamics ◽  
Poisson Bracket ◽  
Mass Density ◽  
Equations Of Motion ◽  
Friedmann Equation ◽  
Noncommutative Space ◽  
Lagrangian Formalism ◽  
Noncommutative Algebra ◽  
Symmetry Properties ◽  
Lagrangian Variables

We propose a new approach in Lagrangian formalism for studying the fluid dynamics on noncommutative space. Starting with the Poisson bracket for single particle, a map from canonical Lagrangian variables to Eulerian variables is constructed for taking into account the noncommutative effects. The advantage of this approach is that the kinematic and potential energies in the Lagrangian formalism continuously change in the infinite limit to the ones in Eulerian formalism and hence make sure that both the kinematical and potential energies are taken into account correctly. Furthermore, in our approach, the equations of motion of the mass density and current density are naturally expressed into conservative form. Based on this approach, the noncommutative Poisson bracket is introduced, and the noncommutative algebra among Eulerian variables and the noncommutative corrections on the equations of motion are obtained. We find that the noncommutative corrections generally depend on the derivatives of potential under consideration. Furthermore, we find that the noncommutative algebra does modify the usual Friedmann equation, and the noncommutative corrections measure the symmetry properties of the density function ρ(z→) under rotation around the direction θ→. This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

2004 ◽  
Vol 126 (1) ◽  
pp. 175-183 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Disk Model ◽  
Sector Model ◽  
Bladed Disk ◽  
Symmetry Properties

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

scholarly journals Composite system in rotationally invariant noncommutative phase space

2018 ◽  
Vol 33 (07) ◽  
pp. 1850037 ◽  
Author(s):  
Kh. P. Gnatenko ◽  
V. M. Tkachuk
Keyword(s):  
Phase Space ◽  
Composite System ◽  
Particle System ◽  
Rotational Symmetry ◽  
Center Of Mass ◽  
Noncommutative Space ◽  
Effective Parameters ◽  
Noncommutative Phase Space ◽  
Noncommutative Algebra ◽  
Rotationally Invariant

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on these conditions, the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.

scholarly journals Gauge-independent Theory of Symmetry. I.

1964 ◽  
Vol 17 (4) ◽  
pp. 431 ◽  
Author(s):  
LJ Tassie ◽  
HA Buchdahl
Keyword(s):  
Electromagnetic Field ◽  
Single Particle ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Conserved Quantities ◽  
Continuous Symmetry ◽  
Symmetry Properties ◽  
Symmetry Transformations ◽  
Hamiltonian Forms

The invariance of a system under a given transformation of coordinates is usually taken to mean that its Lagrangian is invariant under that transformation. Consequently, whether or not the system is invariant will depend on the gauge used in describing the system. By defining invariance of a system to mean the invariance of its equations of motion, a gauge-independent theory of symmetry properties is obtained for classical mechanics in both the Lagrangian and Hamiltonian forms. The conserved quantities associated with continuous symmetry transformations are obtained. The system of a single particle moving in a given electromagnetic field is considered in detail for various symmetries of the electromagnetic field, and the appropriate conserved quantities are found.

scholarly journals THE CONSERVED CHARGES AND INTEGRABILITY OF THE CONFORMAL AFFINE TODA MODELS

1994 ◽  
Vol 09 (30) ◽  
pp. 2783-2801 ◽  
Author(s):  
H. ARATYN ◽  
L. A. FERREIRA ◽  
J. F. GOMES ◽  
A. H. ZIMERMAN
Keyword(s):  
Poisson Bracket ◽  
Equations Of Motion ◽  
Curvature Form ◽  
Two Dimensional ◽  
Conserved Charges ◽  
Zero Curvature ◽  
Algebraic Properties ◽  
Toda Model ◽  
Infinite Sets ◽  
Poisson Commute

We construct infinite sets of local conserved charges for the conformal affine Toda model. The technique involves the abelianization of the two-dimensional gauge potentials satisfying the zero-curvature form of the equations of motion. We find two infinite sets of chiral charges and apart from two lowest spin charges, all the remaining ones do not possess chiral densities. Charges of different chiralities Poisson commute among themselves. We discuss the algebraic properties of these charges and use the fundamental Poisson bracket relation to show that the charges conserved in time are in involution. Connections to other Toda models are established by taking particular limits.

The Nuclear Repulsive-Core Effect as a Possible Consequence of Matter in Interaction with a Classical Relativistic Scalar Field: A New Approach to the Question

1972 ◽  
Vol 50 (7) ◽  
pp. 636-645 ◽  
Author(s):  
D. Leiter ◽  
J. Huschilt ◽  
G. Szamosi
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Hard Core ◽  
Repulsive Core ◽  
Lagrangian Formalism ◽  
Field Equations ◽  
New Formalism ◽  
N Body Problem ◽  
Scalar Field Equations

The N-body problem is analyzed within the framework of a new formalism for relativistic point masses interacting via a scalar field, in which the problems of infinite self-energies are absent. A Lagrangian formalism is exhibited which yields the particle equations of motion in the form of a parameterized class of equations. The parameter determines the choice of boundary conditions which is chosen on the scalar-field equations. The existence or nonexistence of the relativistic nuclear hard-core effect, associated with the scalar-field interactions, is shown to depend critically on the particular set of boundary conditions which are imposed on the scalar-field equations. In particular, time-symmetric boundary conditions yield no hard-core repulsion, while retarded boundary conditions are shown to yield a hard-core repulsion at very short range.

U(2) GAUGE THEORY ON NONCOMMUTATIVE GEOMETRY

2009 ◽  
Vol 24 (15) ◽  
pp. 2889-2897
Author(s):  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Equations Of Motion ◽  
Local Symmetry ◽  
Noncommutative Space ◽  
Gauge Fields ◽  
Zeroth Order ◽  
Field Equations ◽  
Relativistic Analog ◽  
Analog Form ◽  
General Relativistic

We develop a model of gauge theory with U (2) as local symmetry group over a noncommutative space-time. The integral of the action is written considering a gauge field coupled with a Higgs multiplet. The gauge fields are calculated up to the second order in the noncommutativity parameter using the equations of motion and Seiberg-Witten map. The solutions are determined order by order supposing that in zeroth-order they have a general relativistic analog form. The Wu-Yang ansatz for the gauge fields is used to solve the field equations. Some comments on the quantization of the electrical and magnetical charges are also given, with a comparison between commutative and noncommutative cases.

A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Discs

2003 ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
High Efficiency ◽  
Equations Of Motion ◽  
Linear Part ◽  
Forced Response ◽  
Mode Shapes ◽  
Solution Technique ◽  
Nonlinear Structure ◽  
Sector Model ◽  
Symmetry Properties ◽  
Symmetric Structures

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disc using a periodic sector model without any loss of accuracy in calculations and modelling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disc forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disc model: (i) using sector finite element matrices; (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disc with shrouds have demonstrated the high efficiency of the method.

EINSTEIN–MAXWELL–DILATON BLACK BRANES WITH ARBITRARY TENSION AND DILATON CHARGE

2009 ◽  
Vol 24 (10) ◽  
pp. 713-720 ◽  
Author(s):  
IKJAE SHIN ◽  
SANGHEON YUN
Keyword(s):  
Spherical Symmetry ◽  
Mass Density ◽  
Equations Of Motion ◽  
Special Choice ◽  
Dilaton Gravity ◽  
Coupling Constant

In this note, we show that special choice of the metric ansatz simplifies the equations of motion for black branes. Then we use the trick to construct charged, dilatonic black branes of Einstein–Maxwell–dilaton gravity in D = n + p + 2 dimensions, which are invariant under translation along p directions and have spherical symmetry of Sn. The solutions are characterized by mass density and tension, magnetic charges, dilaton charge and coupling constant.

scholarly journals The Effect of Turbulence Modelling on the Assessment of Platelet Activation

2020 ◽  
Author(s):  
Silvia Bozzi ◽  
Davide Dominissini ◽  
Alberto Redaelli ◽  
Giuseppe Passoni
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Models ◽  
Platelet Activation ◽  
Mechanical Heart Valve ◽  
Turbulence Modelling ◽  
Shear Stresses ◽  
Large Variability ◽  
Frequency Distributions ◽  
Lagrangian Variables ◽  
Turbulence Closures

Abstract Pathological platelet activation induced by abnormal shear stresses is regarded as a main clinical complication in recipients of cardiovascular biomedical implantable devices and prostheses. In order to improve their performance computational fluid dynamics (CFD) has been used to evaluate flow fields and related shear stresses. More recently CFD models have been equipped with mathematical models that describe the relation between fluid dynamics variables, and in particular shear stresses, and the platelet activation state (PAS). These mathematical models typically use a Lagrangian approach to extract the shear stresses along possible platelet trajectories. However, in the case of turbulent flow, the choice of the proper turbulence closure model is still debated for both concerning its effect on Lagrangian statistics and shear stress calculation. In our study five numerical simulations of the flow through a mechanical heart valve were performed and then compared in terms of Eulerian and Lagrangian quantities: a direct numerical simulation (DNS), a large eddy simulation (LES), two Reynolds-averaged Navier-Stokes (RANS) simulations (SST k-ω and RSM) and a “Laminar” (no turbulence modelling on a Taylor microscale-based grid) simulation. Results exhibit a large variability in the PAS assessment depending on the turbulence model adopted. “Laminar” and RSM estimates of platelet activation are about 60% below DNS, while LES is 16% less. Surprisingly, PAS estimated from the SST k-ω velocity field is only 8% less than from DNS data. This appears more artificial than physical as can be inferred after comparing frequency distributions of PAS and of the different Lagrangian variables of the mechano-biological model of platelet activation. Our study indicates that turbulence closures can lead to a severe underestimation of platelet activation and suggests that turbulence should be fully resolved by DNS when assessing blood damage in blood contacting devices.

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