Radiation bursts from particles in the field of compact, impenetrable, astrophysical objects

The radiation emitted by charged, scalar particles in a Schwarzschild field with maximal acceleration corrections is calculated classically and in the tree approximation of quantum field theory. In both instances the particles emit radiation that has characteristics similar to those of gamma-ray bursters.     

Casimir Effect for a Perfectly Conducting Wedge in Terms of Local Zeta Function

The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of calculations and gives rise to a finite expression for the energy density in question without any subtractions. Employment of the Hertz potentials for constructing the general solution to the Maxwell equations results in a considerable simplification of the calculations. Transition to the global zeta function is carried out by introducing a cutoff nearby the cusp at the origin. Proceeding from this the heat kernel coefficients are calculated and the high temperature asymptotics of the Helmholtz free energy and of the torque of the Casimir forces are found. The wedge singularity gives rise to a specific high temperature behavior ∼T2 of the quantities under consideration. The obtained results are directly applicable to the free energy of a scalar massless field and electromagnetic field on the background of a cosmic string.     

Some remarks on continuous dependence and uniqueness in finite elastostatics for unbounded domains

Summary In connection with a foregoing paper, in the present note we establish some continuous dependence and uniqueness theorems for classical solutions to the equilibrium problem of finite elasticity. The elastic body is supposed to fill an unbounded domain of the physical space. We employ the weight function method and a suitable extension to the non-linear case of a method previously introduced by other authors for the linear case.

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Sommario In connessione con un precedente lavoro, si dimostrano nella presente nota alcuni teoremi di dipendenza continua ed unicità per soluzioni classiche del problema statico non lineare relativo ad un corpo elastico occupante un dominio illimitato dello spazio fisico. Vengono adoperati il metodo della funzione peso e l'estensione al caso non lineare di un metodo precedentemente introdotto da altri autori per il caso lineare.

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Work performed under the auspices of G.N.F.M. of the Italian Research Council (C.N.R.).     

GSI anomaly and spin–rotation coupling

We propose a model in which a recently reported modulation in the decay of the hydrogenlike ions ¹⁴⁰Pr⁵⁸⁺, ¹⁴²Pm⁶⁰⁺ and ¹²²I⁵²⁺ arises from the coupling of rotation to the spin of electron and nucleus. The model shows that the spin–spin coupling of electron and nucleus does not contribute to the modulation and predicts that the anomaly cannot be observed if the motion of the ions is rectilinear, or if the ions are stopped in a target. It also supports the notion that the modulation frequency is proportional to the inverse of the atomic mass and that no modulation is expected for the β⁺${\beta }^{+}$-decay. The model predicts that for He-like ions the modulation is still present.     

Generalized Uncertainty Principle from QuantumGeometry

The generalized uncertainty principle of string theory is derived in the frameworkof quantum geometry by taking into account the existence of an upper limit onthe acceleration of massive particles.     

Neutrino Oscillations in Caianiello's Quantum Geometry Model

Neutrino flavor oscillations are analyzed in the framework of Quantum Geometry model proposed by Caianiello. In particular, we analyze the consequences of the model for accelerated neutrino particles that experience an effective Schwarzschild geometry modified by the existence of an upper limit on the acceleration, which implies a violation of the equivalence principle. We find a shift of quantum-mechanical phase of neutrino oscillations, which depends on the energy of neutrinos as E³. Implications on atmospheric and solar neutrinos are discussed.     

An asymptotic estimate of the edge effects in the high frequency Kirchhoff diffraction theory for 3-d problems

In the context of wave propagation through a three-dimensional acoustic medium, an analytical approach to estimate the boundary effects in the high-frequency (single) diffraction by thin rigid obstacles is developed. Starting from the classical Kirchhoff (approximate) representation, explicit formulas regarding three sample cases are obtained. The improvement with respect to previous approaches, usually based on refinements of the classical Ray Theory, is evaluated by comparison with the results from a direct numerical solution of the main integrals involved.     

Some results on the energy transmission through an elastic half-space loaded by a periodic distribution of vibrating punches

We develop an analytical approach to study the wave process arising in an elastic half-space because of harmonic vibrations applied on its free surface by a (periodic) distribution of rigid punches. By assuming perfect coupling between punches and half-space, the (in-plane) propagation problem is firstly reduced to a 2×2 system of integral equations for the contact stresses. Then, in the frequency range implying the so-called one-mode (far-field) propagation, suitable mild approximations on the kernels lead to some related auxiliary systems of integral equations, which are independent on frequency and can be solved analytically. The explicit formulas thus obtained are reflected through some figures and enable us to discuss the energetic properties of the wave process with respect to frequency. A direct numerical treatment of the original system of (exact) integral equations confirms the precision of the analytical solution.     

P-wave propagation through elastic solids with a doubly periodic array of cracks

An analytical approach to study normal penetration of a longitudinalplane wave into a doubly periodic array of slit-type obstaclesis developed. By means of suitable assumptions on the physicaland geometrical parameters we arrive at explicit formulae forthe relevant scattering parameters and fields. The underlyingcontext is wave propagation through damaged (elastic) solids.Figures are given which reflect the peculiarities of propagationin such a structure