abstract

The asymptotic behaviour of the solution of a nonlinear dynamical boundary-value problem describing the bio-heat transfer in microvascular tissues is analysed. Our domain \({\mit \Omega }\) is an \(\varepsilon \)-periodic structure, consisting of two parts: a solid tissue part \({\mit \Omega }^{~\varepsilon }\) and small regions of blood \({\mit \Omega }\setminus {\overline {\mit \Omega }^{~\varepsilon }}\) of a certain temperature, \(\varepsilon \) representing a small parameter related to the characteristic size of the blood regions. In such a domain, we shall consider a heat equation, with nonlinear sink and source terms and with a dynamical condition imposed on the boundaries of the blood zones. The limit equation, as \(\varepsilon \rightarrow 0\), is a new heat equation, with extra-terms coming from the influence of the non-homogeneous dynamical boundary condition.

abstract

In this theory, an object is a mass density field in the fabric of space (FS) that satisfies mass–energy equivalence. In contrast with General Relativity (GR), the theory posits a preferred reference frame — namely the reference frame in which the FS is at rest. Also in contrast with GR, gravity between two objects results from the interaction of their mass density fields integrated over the entire FS. This interaction results in two types of gravity: Type I gravity which includes classical gravity, and under certain conditions, Type II gravity which includes a very strong wave gravity. Gravity exerted by large on small objects reduces to classical gravity. Gravity exerted by small on large objects is 3 times the classical value at small kinetic energies. When the small object becomes relativistic, then gravity becomes much larger. Every object has a gravity wavelength, and for the object being acted upon, classical type gravity occurs at distances less than its gravity wavelength while wave gravity occurs at distances greater than its gravity wavelength. The theory yields a set of 8 logarithmic singularities in the gravity force as well as a first-order singularity in the gravity potential. If the FS is quantized into discrete units, these singularities act on the FS to effect changes and interactions in mass density fields instantaneously. As a result, gravity acts instantaneously. We suggest that the 3 degree K cosmic background radiation results from kinetic energy released by the FS units. The theory then predicts that the rest mass of each FS unit is 2 proton masses and its characteristic length is approximately 2 mm. We extend the gravity theory to photons and predict the same results as GR for the classical experimental tests as well as for the change in period of binary pulsars. Finally, we show that the gravity theory makes possible a derivation of the Coulomb force.

abstract

In this paper, we investigate the effects of space noncommutativity and the generalized uncertainty principle on the stability of circular orbits of particles in Schwarzschild spacetime. We show that, up to first order of noncommutativity parameter, an angular momentum dependent extra term will appear in effective potential which affects the stability of circular orbits. In the case of large angular momentum, the condition for stability of circular orbits will change considerably relative to commutative case.

abstract

We show that the existence of the Newtonian limit cannot work as a selection rule for choosing the correct gravity theory from the set of all \(L=f(R)\) gravity theories. To this end we prove that stability of the ground state solution in arbitrary purely metric \(f(R)\) gravity implies the existence of the Newtonian limit of the theory. And the stability is assumed to be the fundamental criterion of viability of any gravity theory. The Newtonian limit is either strict in the mathematical sense if the stable ground state of a theory is flat spacetime, or approximate and valid on length scales much smaller than the cosmological scale if the ground state is de Sitter or anti-de Sitter space. Hence regarding the Newtonian limit a metric \(f(R)\) gravity does not differ from general relativity (with arbitrary \({\mit \Lambda }\)). That stability implies the existence of the Newtonian limit is exceptional to Lagrangians depending on \(R\) and/or the Ricci tensor but not on the Weyl tensor. An independent selection rule is necessary.

abstract

We assume that all quark and lepton mass matrices have upper triangular form. Using all available experimental data on quark and lepton masses and mixing angles we make a fit in which we determine mass matrices elements. There are too many free parameters and our solutions are not unique. We look for solutions with small non diagonal mixing matrix elements. In order to reduce the number of free parameters we assume that the matrix element \((M)_{13}\) vanishes in all mass matrices. Such universal assumption was drawn from considering different numerical solutions. The lepton sector, due to large mixing angles and very small errors for charged lepton masses, is more restrictive then quark sector. We present the solution in this case. The absolute values of neutrino masses are not fixed. Another possibility of reducing number of free parameters was considered by us before. With the additional assumption motivated by SU(5) symmetry which connects mixing in right handed down quarks with left handed charged leptons we get a solution in which observed Cabibbo–Kobayashi–Maskawa mixing for quarks comes mainly from non diagonal terms in up quark mass matrix.

abstract

We propose a simple superpotential for the Higgs doublets, where the electroweak symmetry is broken at the supersymmetric level. We show that, for a class of supersymmetry breaking scenarios, the electroweak scale can be stable even though the supersymmetry breaking scale is much higher than it. Therefore, all the superpartners and the Higgs bosons can be decoupled from the electroweak scale, nevertheless no fine-tuning is needed. We present a concrete model that the required superpotential can indeed be generated dynamically. According to supersymmetry breaking scenarios to be concerned, various phenomenological applications of our model are possible. For example, based on our model, so-called “split supersymmetry” scenario can be realized without fine-tuning. If the electroweak scale supersymmetry breaking is taken into account, our model provides a similar structure to the “fat Higgs” model and the upper bound on the lightest Higgs boson mass can be relaxed.

abstract

In the framework of meson–meson mass mixing matrix and Regge trajectory, in the presence of the \(\eta (1295)\), \(\eta (1475)\) and \(\eta _c(2S)\) being the \(2^1S_0\) meson state, we predict the mass spectrum of the \(2^1S_0\) meson state, and quarkonium content. The decays of isoscalar state are also presented. The results are in good agreement with the values predicted by other theoretical approaches. Our results should be tested in the experiment in the future.

abstract

The wounded quark–diquark model predictions for charged pions multiplicities in PbPb and \(p\)Pb collisions in the central rapidity region at \(\sqrt {s}=17.3\) GeV c.m. energy are presented.

abstract

Intense neutrino beams that accompany muon colliders can be used for interstellar communications. The presence of multi-TeV extraterrestrial muon collider at several light-years distance can be detected after one year run of IceCube type neutrino telescopes, if the neutrino beam is directed towards the Earth. This opens a new avenue in SETI: search for extraterrestrial muon colliders.

abstract

We develop three dimensional (3D) hybrid model of galactic cosmic ray (GCR) propagation in the heliosphere based on the Parker’s transport equation. The hybrid model consists of two parts-stationary for high rigidities of GCR particles and non-stationary for relatively low rigidities. It is supposed that scattering of GCR particles in the irregularities (turbulence) of the interplanetary magnetic field (IMF) can be considered as a Brownian motion, and the Einstein–Smoluchowski relation \(\langle x^{2}\rangle =bKt_{\rm sc}\) is valid; \(\langle x^{2}\rangle \) is the mean-square diffusion distance of the GCR particles, \(K\) is diffusion coefficient and \(t_{\rm sc}\) scattering time; \(b=2, 4\) and 6 for one, two and three dimensional space, respectively. We show that a construction of the hybrid model is possible owing to the dependence of diffusion coefficient on the rigidity of GCR particles. We applied the hybrid model to describe the Forbush effect of the GCR intensity. For the assumed Forbush effect the hybrid model consists of the stationary part for rigidities \(\gt 21\) GV and of the non-stationary part for rigidities \(\lt 21\) GV. This model needs \(\sim 30\)% less time for numerical solution than the non-stationary model.

abstract

Data of neutron monitors have been used to calculate the temporal changes of the power law rigidity spectrum of the long period variations of the galactic cosmic ray (GCR) intensity for two positive \((A\gt 0)\) and two negative \((A\lt 0)\) polarity epochs of solar magnetic cycles (1960–2002). A relationship between the temporal changes of the rigidity spectrum of the long period variations of the GCR intensity and the power spectral density (PSD) of the interplanetary magnetic field (IMF) turbulence has been found. The soft rigidity spectrum of the long period variations of the GCR intensity for the maximum epochs and the hard spectrum for the minimum epochs should be caused by different structure of the IMF turbulence in the range of the frequencies 10\(^{-6}\)–10\(^{-5}\) Hz during the 11-year cycle of solar activity. A noticeable distinction between the temporal changes of the rigidity spectrum for the \(A\gt 0\) and the \(A\lt 0\) polarity epoch is not found. The temporal changes of the exponent of the rigidity spectrum of the long period variations of the GCR intensity should be considered as one of the important (new) indexes to study the 11-year variations of GCR intensity. The new index can be used to determine an exponent of PSD in the energy range 10\(^{-6}\)–10\(^{-5}\) Hz of the IMF turbulence. That region of the IMF turbulence is responsible for the scattering of the GCR particles of 5–50 GV rigidity to which neutron monitors are sensitive.