Integral equation for the interfacial tension of liquid metal in contact with ionic melt

The closed integral equations for the interfacial tension as a function of external polarization at the liquid metal - ionic melt interface are derived. The version of Popel'-Pavlov isotherm is applied to the analysis of electrocapillary curves (ecc), i.e. the dependences of interfacial tension on electrode potential. The interaction between adsorbed particles is taken into account within 'two exchange parameters' approximation. The type of the distribution of electric potential in the double electric layer (del) is assumed to be like 'in series connected capacitors'. The methods of solution are proposed for the analysis of the experimental ecc's.Comment: 8 pages, 3 figures, report at 'HTC (High Temperature Capillarity)' conference, Sanremo, Italy, April 2004, submitted to 'Interface Science

Relaxation and Creep in Twist and Flexure + Addendum to <<Relaxation and Creep in Twist and Flexure>>

The aim of the paper is to derive the exact analytical expressions for torsion and bending creep of rods with the Norton-Bailey, Garofalo and Naumenko-Altenbach-Gorash constitutive models. These simple constitutive models, for example, the time- and strain-hardening constitutive equations, were based on adaptations for time-varying stress of equally simple models for the secondary creep stage from constant load/stress uniaxial tests where minimum creep rate is constant. The analytical solution is studied for Norton-Bailey and Garofalo laws in uniaxial states of stress. The most common secondary creep constitutive model has been the Norton-Bailey Law which gives a power law relationship between minimum creep rate and (constant) stress. The distinctive mathematical properties of the power law allowed the development of analytical methods, many of which can be found in high temperature design codes. The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk springs. The exact analyticalexpressions giving the torque and bending moment as a function of the time were derived

Derivations with Leibniz defect

The non-Leibniz formalism is introduced in this article. The formalism is based on the generalized differentiation operator (kappa-operator) with a non-zero Leibniz defect. The Leibniz defect of the introduced operator linearly depends on one scaling parameter. In a special case, if the Leibniz defect vanishes, the generalized differentiation operator reduces to the common differentiation operator. The kappa-operator allows the formulation of the variational principles and corresponding Lagrange and Hamiltonian equations. The solutions of some generalized dynamical equations are provided closed form.With a positive Leibniz defect the amplitude of free vibration remains constant with time with the fading frequency (>). The negative Leibniz defect leads the opposite behavior, demonstrating the growing frequency (>). However, the Hamiltonian remains constant in time in both cases. Thus the introduction of non-zero Leibniz defect leads to an alternative mathematical description of the conservative systems.Comment: 20 pages, 5 figure

Is it Possible to Describe Economical Phenomena by Methods of Statistical Physics of Open Systems?

The methods of statistical physics of open systems are used for describing the time dependence of economic characteristics (income, profit, cost, supply, currency etc.) and their correlations with each other. Nonlinear equations (analogies of known reaction-diffusion, kinetic, Langevin equation) describing appearance of bifurcations, self-sustained oscillational processes, self-organizations in economic phenomena are offered.Comment: LaTeX, revte

The Multifractal Time and Irreversibility in Dynamic Systems

The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last depends on densities of Lagrangians in a given time moment and in a given point of space. After transition to sets of time points with the integer dimension the obtained equations transfer in the known equations of classical dynamics. Production of an entropy is not equally to zero in space with multifractal time, i.e. the classical systems in this space are non-closed.Comment: RevTe

Physical Consequences of Moving Faster than Light in Empty Space

Physical phenomena caused by particle's moving faster than light in a space with multifractal time with dimension close to integer ($d_{t}=1+\epsilon(r(t),t), |\epsilon| \ll 1$ - time is almost homogeneous and almost isotropic) are considered. The presence of gravitational field is taken into account. According to the results of the developed by the author theory, a particle with the rest energy $E_{0}$ would achieve the velocity of light if given the energy of about $E \sim 10^{3}E_{0}$Comment: RevTeX, 3 page

Does Special Relativity Have Limits of Applicability in the Domain of Very Large Energies?

We have shown in the paper that for time with fractional dimensions (multifractal time theory) there are small domain of velocities $v$ near $v=c$ where SR must be replaced by fractal theory of almost inertial system that do not contains an infinity and permits moving with arbitrary velocities.Comment: LaTex, revte

The Theory of Fractal Time: Field Equations (the Theory of Almost Inertial Systems and Modified Lorentz Transformations)

Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and new fields with imaginary energies .Comment: LaTex2e, revte

Can a Particle's Velocity Exceed the Speed of Light in Empty Space?

Relative motion in space with multifractal time (fractional dimension of time close to integer $d_{t}=1+\epsilon (r,t), \epsilon \ll 1$) for "almost" inertial frames of reference (time is almost homogeneous and almost isotropic) is considered. Presence in such space of absolute frames of reference and violation of conservation laws (though, small because of the smallness of $\epsilon$) due to the openness of all physical systems and inhomogeneiy of time are shown. The total energy of a body moving with $v=c$ is obtained to be finite and modified Lorentz transformations are formulated. The relation for the total energy (and the whole theory) reduce to the known formula of the special relativity in case of transition to the usual time with dimension equal to one.Comment: RevTeX, 4 page

The Theory of Gravitation in the Space - Time with Fractal Dimensions and Modified Lorents Transformations

In the space and the time with a fractional dimensions the Lorents transformations fulfill only as a good approach and become exact only when dimensions are integer. So the principle of relativity (it is exact when dimensions are integer) may be treated also as a good approximation and may remain valid (but modified) in case of small fractional corrections to integer dimensions of time and space. In this paper presented the gravitation field theory in the fractal time and space (based on the fractal theory of time and space developed by author early). In the theory are taken into account the alteration of Lorents transformations for case including $v=c$ and are described the real gravitational fields with spin equal 2 in the fractal time defined on the Riemann or Minkowski measure carrier. In the theory introduced the new "quasi-spin", given four equations for gravitational fields (with different "quasi spins" and real and imaginary energies). For integer dimensions the theory coincide with Einstein GR or Logunov- Mestvirichvili gravitation theory.Comment: LaTex,revte