Term Vanishes Research Articles

Unconventional neutrino mass generation, neutrinoless double beta decays, and collider phenomenology

We study a model in which lepton number violation is solely triggered by a dimension 4 hard breaking term in the scalar potential. A minimal model, which contains a SU(2) triplet with hypercharge Y=2 and a pair of singlet doubly charged scalar fields in addition to the standard model (SM) Higgs doublet, is constructed. The model is technically natural in the sense that lepton number is preserved in the limit that the hard term vanishes. SM phenomenology restricts the vacuum expectation value of the triplet scalar field v{sub T}<5.78 GeV. Neutrino masses controlled by v{sub T} are generated at the two loop level and are naturally in the sub-eV range. In general they exhibit normal hierarchy structure. Here the neutrino mass term does not dominate neutrinoless double beta decays of nuclei. Instead the short-distance physics with doubly charged Higgs exchange gives the leading contribution. We expect weak scale singly and doubly charged Higgs bosons to make their appearances at the LHC and the ILC.

Various kinds of sensitive singular perturbations

We consider variational problems of P. D. E. depending on a small parameter e when the limit process e ↓ 0 implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first time). For each one we prove the sensitive character and we give a formal asymptotics for the behavior e ↓ 0.

MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETO-HYDRODYNAMIC EQUATIONS

The two-dimensional magneto-hydrodynamic (MHD) equations are considered in this article. Viscous approximations are used to obtain the local existence and uniqueness of the classical solution. When the viscous term vanishes, the convergence rates, a main problem in turbulence, are also discussed. Moreover, a blow-up criterion for our classical solution is established in terms of the magnetic fields.

Optical geometry analysis of the electromagnetic self-force

We present an analysis of the behavior of the electromagnetic self-force for charged particles in a conformally static spacetime, interpreting the results with the help of optical geometry. Some conditions for the vanishing of the local terms in the self-force are derived and discussed.

QUASINORMAL MODES FOR ARBITRARY SPINS IN THE SCHWARZSCHILD BACKGROUND

The leading term of the asymptotic of quasinormal modes in the Schwarzschild background, ωn = -in/2, is obtained in two straightforward, analytical ways for arbitrary spins. One of these approaches requires almost no calculations. As simply we demonstrate that for any odd integer spin, described by the Teukolsky equation, the first correction to the leading term vanishes. Then, this correction for half-integer spins is obtained in a slightly more intricate way. Finally, we derive analytically the general expression for the first correction for all spins, described by the Teukolsky equation.

Expansion formulae for the homogenized determinant of anisotropic checkerboards

In this paper, some effective properties of anisotropic four-phase periodic checkerboards are studied in two-dimensional electrostatics. An explicit low-contrast second-order expansion for the determinant of the effective conductivity is given. In the case of a two-phase checkerboard with commuting conductivities, the expansion reduces to an explicit formula for the effective determinant (valid for any contrast) as soon as the second-order term vanishes. Such an explicit formula cannot be extended to four-phase checkerboards. A counter-example with high-contrast conductivities is provided. The construction of the counter-example is based on a factorization principle, due to Astala &amp; Nesi, which allows us to pass from an anisotropic four-phase square checkerboard to an isotropic one with the same effective determinant.

An approach to the Klein–Gordon equation for a dynamic study in ferroelectricmaterials

Ferroelectric materials such as lithium niobate and lithium tantalate show a non-linearhysteresis behaviour, which may be explained by dynamical system analysis. The behaviourof these ferroelectrics is usually explained by domains and domain wall movements. So, thespatial variation of the domain wall was studied previously in order to see its effecton the domain wall width in the context of the Landau–Ginzburg functional.In the present work, both temporal and spatial variations of polarization areconsidered, and by using the Euler–Lagrange dynamical equation of motion, aKlein–Gordon equation is derived by taking the ferroelectrics as a Hamiltoniansystem. An interaction has been considered between the nearest neighbour domains,which are stacked sideways in a parallel array with uniform polarization. Thisinteraction term is associated with the spatial term and when this interaction isassumed to be zero, the spatial term vanishes, giving rise to a Duffing oscillatordifferential equation, which can be also studied by a dynamic system analysis.

Fractal First-Order Partial Differential Equations

The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward the entropy solution of the pure conservation law.

Stable signal recovery from incomplete and inaccurate measurements

AbstractSuppose we wish to recover a vector x0 ∈ ℝ𝓂 (e.g., a digital signal or image) from incomplete and contaminated observations y = A x0 + e; A is an 𝓃 × 𝓂 matrix with far fewer rows than columns (𝓃 ≪ 𝓂) and e is an error term. Is it possible to recover x0 accurately based on the data y?To recover x0, we consider the solution x# to the 𝓁1‐regularization problem where ϵ is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unit‐normed columns) and if the vector x0 is sufficiently sparse, then the solution is within the noise level As a first example, suppose that A is a Gaussian random matrix; then stable recovery occurs for almost all such A's provided that the number of nonzeros of x0 is of about the same order as the number of observations. As a second instance, suppose one observes few Fourier samples of x0; then stable recovery occurs for almost any set of 𝓃 coefficients provided that the number of nonzeros is of the order of 𝓃/(log 𝓂)6.In the case where the error term vanishes, the recovery is of course exact, and this work actually provides novel insights into the exact recovery phenomenon discussed in earlier papers. The methodology also explains why one can also very nearly recover approximately sparse signals. © 2006 Wiley Periodicals, Inc.

Boundary solutions of the two-electron Schrödinger equation at two-particle coalescences of the atomic systems

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper two-electron Schrodinger equation have been derived for both electron-nucleus and electron-electron coalescence. It is shown that the solutions for the electron-nucleus coalescence correspond to the ground and singly excited bound states, including triplet ones. The proper solutions at small distances $R$ from the triple coalescence point were presented as the second order expansion on R and lnR. The vanishing of the Fock's logarithmic terms at the electron-nucleus coalescence line was revealed in the frame of this expansion, unlike the case of electron-electron coalescence. On the basis of the obtained boundary solutions the approximate wave function corresponding to both coalescence lines have been proposed in the two-exponential form with no variational parameters.

Real-time Chern-Simons term for hypermagnetic fields

If non-vanishing chemical potentials are assigned to chiral fermions, then a Chern-Simons term is induced for the corresponding gauge fields. In thermal equilibrium anomalous processes adjust the chemical potentials such that the coefficient of the Chern-Simons term vanishes, but it has been argued that there are non-equilibrium epochs in cosmology where this is not the case and that, consequently, certain fermionic number densities and large-scale (hypermagnetic) field strengths get coupled to each other. We generalise the Chern-Simons term to a real-time situation relevant for dynamical considerations, by deriving the anomalous Hard Thermal Loop effective action for the hypermagnetic fields, write down the corresponding equations of motion, and discuss some exponentially growing solutions thereof.

Multidimensional quasi‐linear diffusion of radiation belt electrons

We consider diffusion of outer zone radiation belt electrons by chorus waves. Quasi‐linear diffusion coefficients valid outside the plasmasphere have only been calculated recently, and indicate that the energy and cross diffusion rates can be comparable to that for pitch angle diffusion. Proper solution of the diffusion equation for phase space density must therefore be based on the full diffusion tensor, but this has been plagued by numerical problems associated with the large and rapidly varying cross terms. To circumvent this, techniques are developed for transforming to variables in which the cross diffusion term vanishes. A model calculation shows significant diffusion of phase space density at L = 4.5 from 0.2 MeV up to a few MeV in less than a day.

Canonical quantization of SU(3) Skyrme model in a general representation

A complete canonical quantization of the SU(3) Skyrme model performed in the collective coordinate formalism in general irreducible representations. In the case of SU(3) the model differs qualitatively in different representations. The Wess-Zumino-Witten term vanishes in all self-adjoint representations in the collective coordinate method for separation of space and time variables. The canonical quantization generates representation dependent quantum mass corrections, which can stabilize the soliton solution. The standard symmetry breaking mass term, which in general leads to representation mixing, degenerates to the SU(2) form in all self-adjoint representations.

The Kontsevich connection on the moduli space of FZZT Liouville branes

We point out that insertions of matrix fields in (connected amputated) amplitudes of (generalized) Kontsevich models are given by covariant derivatives with respect to the Kontsevich moduli. This implies that correlators are sections of symmetric products of the (holomorphic) tangent bundle on the (complexified) moduli space of FZZT Liouville branes. We discuss the relation of Kontsevich parametrization of moduli space with that provided by either the ( p , 1 ) or the ( 1 , p ) boundary conformal field theories. It turns out that the Kontsevich connection captures the contribution of contact terms to open string amplitudes of boundary cosmological constant operators in the ( 1 , p ) minimal string models. The curvature of the connection is of type ( 1 , 1 ) and has delta-function singularities at the points in moduli space where Kontsevich kinetic term vanishes. We also outline the extention of our formalism to the c = 1 string at self-dual radius and discuss the problems that have to be understood to reconciliate first and second quantized approaches in this case.

Asymptotics of the price oscillations of a European call option in a tree model

It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black‐Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/n in the case of usual binomial models since the second term (in ) vanishes. The next term is of type C2(n)/n, with C2(n) some explicit bounded function of n that has no limit when n tends to infinity.

Anomalous magnetic moment of electron in Chern–Simons QED

We calculate the anomalous magnetic moment of the electron in the Chern–Simons theory in 2+1 dimensions with and without a Maxwell term, both at zero temperature as well as at finite temperature. In the case of the Maxwell–Chern–Simons (MCS) theory, we find that there is an infrared divergence, both at zero as well as at finite temperature, when the tree level Chern–Simons term vanishes, which suggests that a Chern–Simons term is essential in such theories. At high temperature, the thermal correction in the MCS theory behaves as 1βlnβM, where β denotes the inverse temperature and M, the Chern–Simons coefficient. On the other hand, we find no thermal correction to the anomalous magnetic moment in the pure Chern–Simons (CS) theory.

Asymptotic behavior of a parabolic-hyperbolic system

We consider a parabolic equation nonlinearly coupled with a damped semilinear wave equation. This system describes the evolution of the relative temperature $\vartheta$ and of the order parameter $\chi$ in a material subject to phase transitions in the framework of phase-field theories. The hyperbolic dynamics is characterized by the presence of the inertial term $\mu\partial_{t t}\chi$ with $\mu>0$. When $\mu=0$, we reduce to the well-known phase-field model of Caginalp type. The goal of the present paper is an asymptotic analysis from the viewpoint of infinite-dimensional dynamical systems. We first prove that the model, endowed with appropriate boundary conditions, generates a strongly continuous semigroup on a suitable phase-space $\mathcal V_0$, which possesses a universal attractor $\mathcal A_\mu$. Our main result establishes that $\mathcal A_\mu$ is bounded by a constant independent of $\mu$ in a smaller phase-space $\mathcal V_1$. This bound allows us to show that the lifting $\mathcal A_0$ of the universal attractor of the parabolic system (corresponding to $\mu=0$) is upper semicontinuous at $0$ with respect to the family $\{\mathcal A_\mu,\mu>0\}$. We also construct an exponential attractor; that is, a set of finite fractal dimension attracting all the trajectories exponentially fast with respect to the distance in $\mathcal V_0$. The existence of an exponential attractor is obtained in the case $\mu=0$ as well. Finally, a noteworthy consequence is that the above results also hold for the damped semilinear wave equation, which is obtained as a particular case of our system when the coupling term vanishes. This provides a generalization of a number of theorems proved in the last two decades.

Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy

AbstractWe consider the behavior of the total energy for the wave equation with the dissipative term. When the dissipative term works well uniformly in every direction, several authors obtain uniform decay estimates of the total energy. On the other hand, if the dissipative term is small enough uniformly in every direction, it is known that there exists a solution whose total energy does not decay. We examine the case that the dissipative term vanishes only in a neighborhood of a half-line. We introduce a uniform decay property, which is a natural generalization of the uniform decay estimates, and show that this property does not hold in our case. We prove this by constructing asymptotic solutions supported in the place where the dissipative term vanishes.

Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites

We extend the previous approach of one of the authors on exact strong-contrast expansions for the effective conductivity σe of d-dimensional two-phase composites to case of macroscopically isotropic composites consisting of N phases. The series consists of a principal reference part and a fluctuation part (a perturbation about a homogeneous reference or comparison material), which contains multipoint correlation functions that characterize the microstructure of the composite. The fluctuation term may be estimated exactly or approximately in particular cases. We show that appropriate choices of the reference phase conductivity, such that the fluctuation term vanishes, results in simple expressions for σe that coincide with the well-known effective-medium and Maxwell approximations for two-phase composites. We propose a simple three-point approximation for the fluctuation part, which agrees well with a number of analytical and numerical results, even when the contrast between the phases is infinite near percolation thresholds. Analytical expressions for the relevant three-point microstructural parameters for certain mixed coated and multicoated spheres assemblages (extensions of the Hashin–Shtrikman coated-spheres assemblage) are given. It is shown that the effective conductivity of the multicoated spheres model can be determined exactly.

Small-angle scattering in a marginal Fermi liquid

We study the magnetotransport properties of a model of small-angle scattering in a marginal Fermi liquid. Such a model has been proposed by Varma and Abrahams [Phys. Rev. Lett. 86, 4652 (2001)] to account for the anomalous temperature dependence of in-plane magnetotransport properties of the high-Tc cuprates. We study the resistivity, Hall angle and magnetoresistance using both analytical and numerical techniques. We find that small-angle scattering only generates a new temperature dependence for the Hall angle near particle-hole symmetric Fermi surfaces where the conventional Hall term vanishes. The magnetoresistance always shows Kohler's rule behavior.