Outer curvature and conformal geometry of an imbedding

The differential geometry of an imbedded (e.g. string or membrane world sheet) surface in a higher-dimensional background is shown to be conveniently describable (except in the null limit case) in terms of what are designated as its first, second, and third fundamental tensors, which will have the respective symmetry properties η_μν = η_(μν) as a trivial algebraic identity, K_μν^ρ = K_(μν)^ρ as the “generalised Weingarten identity”, which is the (Frobenius type) integrability condition for the imbedding, and Ξ_λμν^ρ = Ξ_(λμν)^ρ as a “generalised Codazzi equation”, which depends on the background geometry being flat or of constant curvature, needing replacement by a more complicated expression for a generic value of the background curvature B_κλ^μ_ν. The “generalised Gauss equation” expressing the dependence on this background curvature of the internal curvature tensor R_κλ^μ_ν of the imbedded surface is converted into terms of the first and second fundamental tensors, and it is thereby demonstrated that the vanishing of the (conformally invariant) “conformation tensor”, i.e. the trace free part C_μν^ρ of the second fundamental tensor K_μv^ρ, is a sufficient condition for conformal flatness of the imbedded surface (and thus in particular for the vanishing of its (Weyl type) conformal curvature tensor C_κλ^μ_ν) provided the background is itself conformally flat. In a trio of which the first two members are the generalised Gauss and Codazzi equations, the “third” member is shown to give an expression in terms of C_μν^ρ for the (trace free, conformally invariant) “outer curvature” tensor Ω_κλ^μ_ν whose vanishing is the condition for feasibility of the natural generalisation of the Walker frame transportation ansatz. The vanishing of C_μν^ρ is shown to be sufficient in a conformally flat background for the vanishing also of Ω_κλ^μ_ν.     

The Riemann surface in the target space and vice versa

It is observed that the classical part of the partition function associated with the mappings from a genus-g Reimann surface Σ_g to an “almost complex” target space T_2d is equal to that related to the mappings Σ_d to T_2g. The classical part related to the mappings from a genus-2g Reimann surface Σ_2g described by a “real” period matrix, to a target space T_d is equal to the classical part related to mappings from Σ_2g to T_g. Some physical consequences of these mathematical identities are discusses.     

Consequences for nuclear physics of a NNγ and A NNγ time reversal violating vertex

This paper studies the effects in low energy nuclear physics of a possible time reversal invariance (TRI) violation in the electromagnetic interaction. It is shown that this effect appears as a two body short range TRI violating transition operator or as a two and three body TRI violating potential. Two cases are studied. Firstly a TRI violating NNγ vertex is considered and found to have very little effect. Secondly the TRI violation is assumed to occur in the NN^*γ vertex and it is shown that if the violation is “maximal” the contribution to the imaginary part of the “mixing ratio” δ is Im δ ≈ ¦δ¦ × 10⁻³. This should be measurable.     

Methane activation over Ag-exchanged ZSM-5 zeolites: A theoretical study

Methane activation catalyzed over Ag-exchanged ZSM-5 zeolites was investigated by using the density functional theory (DFT) with a cluster model. Two different pathways were taken into account in this work: the “alkyl” and the “carbenium” pathways. The activation barriers obtained are 34.09 and 66.63 kcal/mol for the “alkyl” and the “carbenium” pathway, respectively. The calculated results show that the activation barrier of the “alkyl” pathway is smaller than that of “carbenium” pathway. Consequently, the “alkyl” pathway is the preferential reaction pathway. A new mechanism of methane conversion in the presence of ethene was proposed. In the catalytic cycle, the initial step of methane activation proceeds with the “alkyl” pathway and the Ag⁺ cation acts as an acceptor of the methyl group, then ethene reacts with the Ag⁺CH₃⁻ group to form propene. In addition, it is found that the Ag⁺ cations play an important role in the methane activation, compared with the reaction of methane activation over H-ZSM-5.     

Nonconservation of total lepton number with scalar bosons

The role of scalar bosons is studied in connection with a violation of the number of fermions + antifermions. Some simple estimates of the transitions μ → eλ and μ → 3e are based upon a minimal extension of the “standard” gauge model of weak and electromagnetic interactions.     

WZW–Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson σ-model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting “WZW–Poisson” manifold M is characterized by a bivector Π and by a closed three-form H such that 1/2[Π,Π]_Schouten=H,ΠΠΠ.     

3ν oscillations in matter and solar neutrino data

A method of searching for 3ν solutions of the solar neutrino problem in terms of 2ν solutions is proposed. It gives “iso-SNU strips” on the plot of Δm² versus sin²2θ. A combined analusis of Cl---Ar experiment data and results of the ⁸B neutrino flux measurement by νe scattering (Kamiokande II) is presented.     

Standing wave treatment applied to 3-level bistable system

A c-number treatment for the standing (plane) wave effects in a bistable system placed in a Fabry-Perot cavity is employed without “truncation of hierarchy” or “spatial average” procedure. The specific example of the 3-level Lambda-shape (two-photon) system is illustrated.     

Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Long-time correlation tails in crystals

Nonequilibrium thermodynamics and the Onsager hypothesis are utilized to demonstrate that long-time correlation “tails”, decaying as t^−3/2, should be expected in the velocity autocorrelation function of crystals. In the simplest situation, this behavior is due to the non-propagating (Rayleigh) mode. In the general case, it is argued that “diffusive” modes decaying in wavevector space as exp (−tK²), where is a constant, should lead to the same behavior.     

Acoustic Analyses of Developmental Changes and Emotional Expression in the Preverbal Vocalizations of Infants

The nonverbal vocal utterances of seven normally hearing infants were studied within their first year of life with respect to age- and emotion-related changes. Supported by a multiparametric acoustic analysis it was possible to distinguish one inspiratory and eleven expiratory call types. Most of the call types appeared within the first two months; some emerged in the majority of infants not until the 5th (“laugh”) or 7th month (“babble”). Age-related changes in acoustic structure were found in only 4 call types (“discomfort cry,” “short discomfort cry,” “wail,” “moan”). The acoustic changes were characterized mainly by an increase in harmonic-to-noise ratio and homogeneity of the call, a decrease in frequency range and a downward shift of acoustic energy from higher to lower frequencies. Emotion-related differences were found in the acoustic structure of single call types as well as in the frequency of occurrence of different call types. A change from positive to negative emotional state was accompanied by an increase in call duration, frequency range, and peak frequency (frequency with the highest amplitude within the power spectrum). Negative emotions, in addition, were characterized by a significantly higher rate of “crying,” “hic” and “ingressive vocalizations” than positive emotions, while positive emotions showed a significantly higher rate of “babble,” “laugh,” and “raspberry.”     

Retrieval of cirrus particle sizes using a split-window technique: a sensitivity study

This paper examines the sensitivity of retrieved ice particle sizes using split-window method to the light scattering program for the single scattering calculation. We find that for randomly oriented hexagonal ice particles the retrieval algorithm using the anomalous diffraction theory (ADT) significantly overestimates the mean effective ice particle sizes, D_ge. The retrieved D_ge based on the geometric optics method (GOM) and Mie theory agrees with reference results within 20% when D_ge<30 μm. Based on the speculation that there is no “tunneling” for complex particles, some recent studies suggest that the ADT is an appropriate method to simulate the absorption coefficient for irregularly shaped particles in the infrared. In this study, however, we find that the overestimation of D_ge due to the ADT is largely caused by the neglect of refraction and reflection processes, instead of by the neglect of “tunneling” in the absorption calculations. By considering complex particle shapes such as aggregates with surface roughness, we further find that the retrieved D_ge based on the GOM is not sensitive to the particle shapes. Note that both ADT and GOM do not consider the “tunneling”, but the retrieved D_ge based on the ADT is about two times larger than those based on the GOM. “Tunneling” plays a significant role in the retrieved D_ge only when the D_ge is larger than 30–35 μm. In this study, we also examine the sensitivities of retrieved D_ge to the ice particle size distributions assumed in the retrieval algorithm and to the errors in the emissivities. It is found that when the D_ge is larger than 30–40 μm, the retrieved D_ge becomes very sensitive to the uncertainties related to the ice particle size distributions and to the errors in cirrus emissivities derived from measurements.     

Nuclear track radiography of “Hot” aerosol particles

Nuclear track radiography was applied to identify aerosol “hot” particles which contain elements of nuclear fuel and fallout after Chernobyl NPP accident. For the determination of the content of transuranium elements in radioactive aerosols the measurement of the -activity of “hot” particles by SSNTD was used in this work, as well as radiography of fission fragments formed as a result of the reactions (n,f) and (γ,f) in the irradiation of aerosol filters by thermal neutrons and high energy gamma quanta. The technique allowed the sizes and alpha-activity of “hot” particles to be determined without extracting them from the filter, as well as the determination of the uranium content and its enrichment by ²³⁵U, ²³⁹Pu and ²⁴¹Pu isotopes. Sensitivity of determination of alpha activity by fission method is 5×10⁻⁶ Bq per particle. The software for the system of image analysis was created. It ensured the identification of track clusters on an optical image of the SSNTD surface obtained through a video camera and the determination of size and activity of “hot” particles.     

Electron-muon permutation symmetry and multiplicatively conserved lepton number in gauge theories

The similarity between the weak interactions of electron and muon is extended to the principle that all e and μ interactions in gauge models are invariant under e ↔ μ exchange. This necessitates the existence of two Higgs doublets φ_e and φ_μ, and an extended e ↔ μ permutation invariance. After symmetry-breaking, a multiplicatively conserved “permutation parity” π = ± 1 for all particles naturally emerges, with π_μ = −π_e = 1. The model forbids μ → eγ but predicts e⁻e⁻ → μ⁻μ⁻ mediated by π = −1 Higgs bosons at 10⁻¹¹ times the rate of typical weak cross sections.     

Divisors on elliptic Calabi-Yau 4-folds and the superpotential in F-theory — I

Each smooth elliptic Calabi-Yau 4-fold determines both a three-dimensional physical theory (a compactification of “M-theory”) and a four-dimensional physical theory (using the “F-theory” construction). A key issue in both theories is the calculation of the “superpotential” of the theory, which by a result of Witten is determined by the divisors D on the 4-fold satisfying X( _D = 1. We propose a systematic approach to identify these divisors, and derive some criteria to determine whether a given divisor indeed contributes. We then apply our techniques in explicit examples, in particular, when the base B of the elliptic fibration is a toric variety or a Fano 3-fold.

When B is Fano, we show how divisors contributing to the superpotential are always “exceptional” (in some sense) for the Calabi-Yau 4-fold X. This naturally leads to certain transitions of X, i.e., birational tranformations to a singular model (where the image of D no longer contributes) as well as certain smoothings of the singular model. The singularities which occur are “canonical”, the same type of singularities of a (singular) Weierstrass model. We work out the transitions. If a smoothing exists, then the Hodge numbers change.

We speculate that divisors contributing to the superpotential are always “exceptional” (in some sense) for X, also in M-theory. In fact we show that this is a consequence of the (log)-minimal model algorithm in dimension 4, which is still conjectural in its generality, but it has been worked out in various cases, among which are toric varieties.     

Photoproduction of Θ and other pentaquark states

We present constraints on the relative photoproduction cross sections of positive parity pentaquark states, Σ₅, Λ₅, and N₅, based on a minimum phenomenology gained in and their baryon–meson couplings as in the work of Close and Dudek. The possibility of anomalous signals in γp→K⁰_S(Θ⁺;Σ_d⁺) is discussed. We emphasize the importance of comparing with “conventional” states such as γN→KΣ(1660).     

Development of Bragg grating sensors at CEFET-PR

A report of activities in the development of fibre optic Bragg grating (FOBG) sensors at “Centro Federal de Educação Tecnológica do Paraná (CEFET-PR)” is given. Numerical simulation, experimental development, calibration procedures and application results are used to study FOBG sensors in mechanical, electrical and biomedical engineering.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Itinerant-localized duality description of the spin fluctuations in the normal state of high-Tc cuprates. An explanation of neutron scattering experiments

On the basis of the itinerant-localized duality theory of spin fluctuations, the puzzling aspects of the neutron scattering experiments in the normal state of high-T_c cuprates are clarified from a global point of view. The dynamical spin structure factor exhibits two different aspects depending on the energy transfer ω. At lower energies, ω < ω_c, where ω_c is the fermion coherence energy, the spectrum is coherent so that the characteristic scales for wavevector and energy are temperature dependent, while at higher energies, ω > ω_c, the spectrum is incoherent so that those characteristic scales are temperature independent. The integrated weight of the coherent part of the spectrum exhibits the so-called “spin gap” behavior when the Fermi surface of the itinerant fermion is technically nested, even though there is no excitation gap in the spectrum at all.