arXiv subjects
Publications and source records attributed to Amir H. Fatollahi.
Using an identity, directly derived from the Young-Laplace equation, the problem of the equilibrium shape of an axisymmetric sessile drop is reduced to a one-parameter shooting method problem. Based on the method the numerical solutions for drops with Bond number up to 15 are plotted. The agreement between the method and the ADSA-D method as well as the experimental data is tested. A Mathematica code based on the method is presented.
The shape of drop on a flat horizontal plane is obtained by including the first order of correction by the weight. The sphere solution of the weightless drop is used to introduce a new polar coordinate by which the perturbative expression for a region of a drop can be extended analytically to the entire surface of a drop having both the concave and the convex parts. Comparison with experimental data are presented.
It is shown that as far as the linear diffusion equation meets both time- and space- translational invariance, the time dependence of a moment of degree $α$ is a polynomial of degree at most equal to $α$, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.
The problem of black-body radiation is considered in the Born-Infeld theory of electrodynamics. In particular, at 2-loop order the deviation from the Planck expression due to the self-interaction of photons is calculated. It is seen that the system of interacting photons of the theory, opposed to its non-Abelian counterpart, has higher internal energy at this order of perturbation. Possible implications of the result on the evolution of very hight temperature systems, including various stellar media and the early universe, are briefly discussed.
The nonrelativistic quark model predicts that the spin and the magnetic moment of proton are not parallel. Based on, the modifications are outlined that sound crucial for the analysis of the data out of scattering off the protons.
A complete classification is given for one dimensional chains with nearest neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem via the Euler parameterization is also presented. SU(2)-invariant systems are discussed, and the corresponding eigenvalue problem for the Hamiltonian is reduced to an ordinary differential equation, as it is the case with such models on commutative spaces.
The Poisson structure is constructed for a model in which spatial coordinates of configuration space are noncommutative and satisfy the commutation relations of a Lie algebra. The case is specialized to that of the group SU(2), for which the counterpart of the angular momentum, as well as the Euler parameterization of the phase space are introduced. SU(2)-invariant classical systems are discussed, and it is observed that the path of particle can be obtained by the solution of a first-order equation, as the case with such models on commutative spaces. The examples of free particle, rotationally-invariant potentials, and specially the isotropic harmonic oscillator are investigated in more detail.
The emergent gravity proposal is examined within the framework of noncommutative QED/gravity correspondence from particle dynamics point of view.
The possibility is examined that a model based on space noncommutativity of linear type can explain why photons from distant sources with multi-TeV energies can reach earth. In particular within a model in which space coordinates satisfy the algebra of SU(2) Lie group, it is shown that there is the possibility that the pair production through the reaction of CMB and energetic photons would be forbidden kinematically.
It is argued that demanding for similar characters between the coordinates of space-time and the fields would sound that non-Abelian gauge theories might be formulated most naturally based on fields depending on matrix coordinates.
Including loop corrections, black-body radiation in noncommutative space is anisotropic. A direct implication of possible space noncommutativity on the Cosmic Microwave Background map is argued.
We consider the possibility that photons of noncommutative QED can make bound states. Using the potential model, developed based on the constituent gluon picture of QCD glue-balls, arguments are presented in favor of existence of these bound states. The basic ingredient of potential model is that the self-interacting massless gauge particles may get mass by inclusion non-perturbative effects.
One approach for formulating the classical dynamics of charged particles in non-Abelian gauge theories is due to Wong. Following Wong's approach, we derive the classical equations of motion of a charged particle in U(1) gauge theory on noncommutative space, the so-called noncommutative QED. In the present use of the procedure, it is observed that the definition of mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of charges in noncommutative space.
It is argued that the internal dynamics of a baryon, as a bound state of QCD-strings and quarks, may be captured by a theory of matrix coordinates.
It is argued that one natural choice for coordinates of constituents of a baryonic state in a SU(N) gauge theory are N x N hermitian matrices. It is discussed that the relevance of matrix coordinates is supported at least by the restricted form of the color symmetry. Based on the previous investigations in this direction, the consequences of the idea are shortly reviewed. The model has been considered is originated by the D0-branes of String Theory.
We consider the dynamics of a charged particle in a space whose coordinates are $N\times N$ hermitian matrices. Putting things in the framework of D0-branes of String Theory, we mention that the transformations of the matrix coordinates induce non-Abelian transformations on the gauge potentials. The Lorentz equations of motion for matrix coordinates are derived, and it is observed that the field strengths also transform like their non-Abelian counterparts. The issue of the map between theory on matrix space and ordinary non-Abelian gauge theory is discussed. The phenomenological aspect of "finite-N non-commutativity" for the bound states of D0-branes appears to be very attractive.
We consider the problem of the interaction between D0-brane bound state and 1-form RR photons by the world-line theory. Based on the fact that in the world-line theory the RR gauge fields depend on the matrix coordinates of D0-branes, the gauge fields also appear as matrices in the formulation. At the classical level, we derive the Lorentz-like equations of motion for D0-branes, and it is observed that the center-of-mass is colourless with respect to the SU(N) sector of the background. Using the path integral method, the perturbation theory for the interaction between the bound state and the RR background is developed. We discuss what kind of field theory may be corresponded to the amplitudes which are calculated by the perturbation expansion in world-line theory. Qualitative considerations show that the possibility of existence of a map between the world-line theory and the non-Abelian gauge theory is very considerable.