Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge

Log-periodic route to fractal functions

Log-periodic oscillations have been found to decorate the usual power law behavior found to describe the approach to a critical point, when the continuous scale-invariance symmetry is partially broken into a discrete-scale invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes characterized by the amplitudes A(n) of the power law series expansion. These two classes are separated by a novel ``critical'' point. Growth processes (DLA), rupture, earthquake and financial crashes seem to be characterized by oscillatory or bounded regular microscopic functions g(x) that lead to a slow power law decay of A(n), giving strong log-periodic amplitudes. In contrast, the regular function g(x) of statistical physics models with ``ferromagnetic''-type interactions at equibrium involves unbound logarithms of polynomials of the control variable that lead to a fast exponential decay of A(n) giving weak log-periodic amplitudes and smoothed observables. These two classes of behavior can be traced back to the existence or abscence of ``antiferromagnetic'' or ``dipolar''-type interactions which, when present, make the Green functions non-monotonous oscillatory and favor spatial modulated patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new demonstration of the source of strong log-periodicity and of a justification of the general offered classification, update of reference lis

Addressing \mu-b_\mu and proton lifetime problems and active neutrino masses in a U(1)^\prime-extended supergravity model

We present a locally supersymmetric extension of the minimal supersymmetric Standard Model (MSSM) based on the gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y\times U(1)^\prime$ where, except for the supersymmetry breaking scale which is fixed to be $\sim 10^{11}$ GeV, we require that all non-Standard-Model parameters allowed by the {\it local} spacetime and gauge symmetries assume their natural values. The $U(1)^\prime$ symmetry, which is spontaneously broken at the intermediate scale, serves to ({\it i}) explain the weak scale magnitudes of $\mu$ and $b_\mu$ terms, ({\it ii}) ensure that dimension-3 and dimension-4 baryon-number-violating superpotential operators are forbidden, solving the proton-lifetime problem, ({\it iii}) predict {\it bilinear lepton number violation} in the superpotential at just the right level to accommodate the observed mass and mixing pattern of active neutrinos (leading to a novel connection between the SUSY breaking scale and neutrino masses), while corresponding trilinear operators are strongly supppressed. The phenomenology is like that of the MSSM with bilinear R-parity violation, were the would-be lightest supersymmetric particle decays leptonically with a lifetime of $\sim 10^{-12}-10^{-8}$ s. Theoretical consistency of our model requires the existence of multi-TeV, stable, colour-triplet, weak-isosinglet scalars or fermions, with either conventional or exotic electric charge which should be readily detectable if they are within the kinematic reach of a hadron collider. Null results of searches for heavy exotic isotopes implies that the re-heating temperature of our Universe must have been below their mass scale which, in turn, suggests that sphalerons play a key role for baryogensis. Finally, the dark matter cannot be the weakly interacting neutralino.Comment: 33 pages, 2 figures, Discussion on proton decay and radiative neutrino masses augmented, and references adde

Anisotropic thermal expansion and magnetostriction of YNi2_2B2_2C single crystals

We present results of anisotropic thermal expansion and low temperature magnetostriction measurements on YNi$_2$B$_2$C single crystals grown by high temperature flux and floating zone techniques. Quantum oscillations of magnetostriction were observed at low temperatures for $H \| c$ starting at fields significantly below $H_{c2}$ ($H < 0.7 H_{c2}$). Large irreversible, longitudinal magnetostriction was seen in both, in-plane and along the c-axis, directions of the applied magnetic field in the intermediate superconducting state. Anisotropic uniaxial pressure dependencies of $T_c$ were evaluated using results of zero field, thermal expansion measurements

Recombinant snakebite antivenoms: A cost-competitive solution to a neglected tropical disease?

Snakebite envenoming is a major public health burden in tropical parts of the developing world. In sub-Saharan Africa, neglect has led to a scarcity of antivenoms threatening the lives and limbs of snakebite victims. Technological advances within antivenom are warranted, but should be evaluated not only on their possible therapeutic impact, but also on their cost-competitiveness. Recombinant antivenoms based on oligoclonal mixtures of human IgG antibodies produced by CHO cell cultivation may be the key to obtaining better snakebite envenoming therapies. Based on industry data, the cost of treatment for a snakebite envenoming with a recombinant antivenom is estimated to be in the range USD 60-250 for the Final Drug Product. One of the effective antivenoms (SAIMR Snake Polyvalent Antivenom from the South African Vaccine Producers) currently on the market has been reported to have a wholesale price of USD 640 per treatment for an average snakebite. Recombinant antivenoms may therefore in the future be a cost-competitive alternative to existing serum-based antivenoms

Anaerobic digestion of manure - consequences for plant production

Organic farming systems are today dependent upon fossil energy. Another challenge are soil nutrient concentrations, which may be depleted with time even in animal husbandry systems (Løes & Øgaard 2001). Anaerobic digestion (AD) of animal manure may produce biogas to replace fossil fuels, and reduce methane (CH4) emissions during manure storage. Co-digestion of substrates rich in energy increases the economic viability of the biogas plant, and off-farm substrates such as fish silage or household waste may add nutrients to the farming system. AD may also ease manure handling, while reducing the amount of weed seeds and animal pathogens. A reduced proportion of easily degraded C in the AD-manure may however impact the soil fauna/microflora and humus levels. Mineralization of organic N during AD may increase nutrient availability and crop yields. Possibly, the increased levels of root and shoot residues may compensate for the organic C removed via AD

Shape Distortion by Irreversible Flux-Pinning-Induced Magnetostriction

Exact analytical results are obtained for the flux-pinning-induced magnetostriction in cylindrical type-II superconductors placed in parallel magnetic field. New modes of irreversible deformation are found: In contrast to the circular cylinder where shape is conserved, it is shown that a square cross-section deforms with considerable distortion. During a field cycle both concave, convex, and even more complicated distortions are predicted. Strong implications for dilatometric measurements on crystals are emphasized. The main results are valid for any critical-state model, j_c = j_c(B).Comment: 4 pages, 4 graph

Mechanism for flux guidance by micrometric antidot arrays in superconducting films

A study of magnetic flux penetration in a superconducting film patterned with arrays of micron sized antidots (microholes) is reported. Magneto-optical imaging (MOI) of a YBCO film shaped as a long strip with perpendicular antidot arrays revealed both strong guidance of flux, and at the same time large perturbations of the overall flux penetration and flow of current. These results are compared with a numerical flux creep simulation of a thin superconductor with the same antidot pattern. To perform calculations on such a complex geometry, an efficient numerical scheme for handling the boundary conditions of the antidots and the nonlocal electrodynamics was developed. The simulations reproduce essentially all features of the MOI results. In addition, the numerical results give insight into all other key quantities, e.g., the electrical field, which becomes extremely large in the narrow channels connecting the antidots.Comment: 8 pages, 7 figure

The tetralogy of Birkhoff theorems

We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement that the gravitational far-field of a spherically symmetric star carries, apart from its mass, no information about the star; therefore, a radially oscillating star has a static gravitational far-field. Third, in mathematical physics, Birkhoff's theorem reads: up to singular exceptions of measure zero, the spherically symmetric solutions of Einstein's vacuum field equation with Lambda = 0 can be expressed by the Schwarzschild metric; for Lambda unequal 0, it is the Schwarzschild-de Sitter metric instead. Fourth, in differential geometry, any statement of the type: every member of a family of pseudo-Riemannian space-times has more isometries than expected from the original metric ansatz, carries the name Birkhoff-type theorem. Within the fourth of these classes we present some new results with further values of dimension and signature of the related spaces; including them are some counterexamples: families of space-times where no Birkhoff-type theorem is valid. These counterexamples further confirm the conjecture, that the Birkhoff-type theorems have their origin in the property, that the two eigenvalues of the Ricci tensor of two-dimensional pseudo-Riemannian spaces always coincide, a property not having an analogy in higher dimensions. Hence, Birkhoff-type theorems exist only for those physical situations which are reducible to two dimensions.Comment: 26 pages, updated references, minor text changes, accepted by Gen. Relat. Gra