Multipole Moments of Fractal Distribution of Charges

In this paper we consider the electric multipole moments of fractal distribution of charges. To describe fractal distribution, we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. In the paper we compute the electric multipole moments for homogeneous fractal distribution of charges.Comment: LaTeX, 11 page

Nullspaces and frames

In this paper we give new characterizations of Riesz and conditional Riesz frames in terms of the properties of the nullspace of their synthesis operators. On the other hand, we also study the oblique dual frames whose coefficients in the reconstruction formula minimize different weighted norms.Comment: 16 page

Spectrally pure heralded single photons by spontaneous four-wave mixing in a fiber: reducing impact of dispersion fluctuations

We model the spectral quantum-mechanical purity of heralded single photons from a photon-pair source based on nondegenerate spontaneous four-wave mixing taking the impact of distributed dispersion fluctuations into account. The considered photon-pair-generation scheme utilizes pump-pulse walk-off to produce pure heralded photons and phase matching is achieved through the dispersion properties of distinct spatial modes in a few-mode silica step-index fiber. We show that fiber-core-radius fluctuations in general severely impact the single-photon purity. Furthermore, by optimizing the fiber design we show that generation of single photons with very high spectral purity is feasible even in the presence of large core-radius fluctuations. At the same time, contamination from spontaneous Raman scattering is greatly mitigated by separating the single-photon frequency by more than 32 THz from the pump frequency

High temperature thermoelectric efficiency in Ba8Ga16Ge30

The high thermoelectric figure of merit (zT) of Ba8Ga16Ge30 makes it one of the best n-type materials for thermoelectric power generation. Here, we describe the synthesis and characterization of a Czochralski pulled single crystal of Ba8Ga16Ge30 and polycrystalline disks. Measurements of the electrical conductivity, Hall effect, specific heat, coefficient of thermal expansion, thermal conductivity, and Seebeck coefficient were performed up to 1173 K and compared with literature results. Dilatometry measurements give a coefficient of thermal expansion of 16×10^−6 K^−1 up to 1175 K. The trend in electronic properties with composition is typical of a heavily doped semiconductor. The maximum in the thermoelectric figure of merit is found at 1050 K with a value of 0.8. The correction of zT due to thermal expansion is not significant compared to the measurement uncertainties involved. Comparing the thermoelectric efficiency of segmented materials, the effect of compatibility makes Ba8Ga16Ge30 more efficient than the higher zT n-type materials SiGe or skutterudite CoSb3

Electromagnetic field of fractal distribution of charged particles

Electric and magnetic fields of fractal distribution of charged particles are considered. The fractional integrals are used to describe fractal distribution. The fractional integrals are considered as approximations of integrals on fractals. Using the fractional generalization of integral Maxwell equation, the simple examples of the fields of homogeneous fractal distribution are considered. The electric dipole and quadrupole moments for fractal distribution are derived.Comment: RevTex, 21 pages, 2 picture

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

Validation and analysis of regional present-day climate and climate change simulations over Europe

In the European Commission (EC) project "Regionalization of Anthropogenic Climate Change Simulations, RACCS, recently terminated, 11 European institutions have carried out tests of dynamical and statistical regionalization techniques. The outcome of the "dynamical part" of the project, utilizing a series of high resolution LAMs and a variable resolution global model (all of which we shall refer to as RCMs, Regional Climate Models), is presented here. The per- formance of the dqterent LAMs had first, in a preceding EC project, been tested with "perfect" boundary forcing fields (ECMWF analyses) and also multi-year present-day climate simula- tions with AMIP "perfect ocean " or mixed layer ocean GCM boundary conditions had been validated against available climatological data. The present report involves results of vali- dation and analysis of RCM present-day climate simulations and anthropogenic climate change experiments. Multi-year (5 - 30 years) present-day climate simulations have been per- formed with resolutions between 19 and 70 km (grid lengths) and with boundary conditions from the newest CGCM simulations. The climate change experiments involve various 2xCO2 - ]xCO2 transient greenhouse gas experiments and in one case also changing sulphur aerosols. A common validation and inter-comparison was made at the coordinating institution, MPIfor Meteorology. The validation of the present-day climate simulations shows the importance of systematic errors in the low level general circulation. Such errors seem to induce large errors in precipitation and surface air temperature in the RCMs as well as in the CGCMs providing boundary conditions. Over Europe the field of systematic errors in the mean sea level pressure (MSLP) usually involve an area of too low pressure, often in the form of an east-west trough across Europe with too high pressure to the north and south. New storm-track analyses confirm that the areas of too low pressure are caused by enhanced cyclonic activity and similarly that the areas of too high pressure are caused by reduced such activity. The precise location and strength of the extremes in the MSLP error field seems to be dependent on the physical param- eterization package used. In model pairs sharing the same package the area of too low pressure is deepened further in the RCM compared to the corresponding CGCM, indicating an increase of the excessive cyclonic activity with increasing resolution. From the experiments performed it seems not possible to decide to what extent the systematic errors in the general circulation are the result of local errors in the physical parameterization schemes or remote errors trans- mitted to the European region via the boundary conditions. Additional errors in precipitation and temperature seems to be due to direct local effects of errors in certain parameterization schemes and errors in the SSTs taken from the CGCMs. For all seasons many biases are fOund to be statistically significant compared to estimates of the internal model variability of the time- slice mean values. In the climate change experiments statistically significant European mean temperature changes which are large compared to the corresponding biases are found. How- ever, the changes in the deviations from the European mean temperature as well as the changes in precipitation are only partly sign wcan ce and are of the same order of magnitude or smaller than the corresponding biases found in the present-day climate simulations. Cases of an inter- action between the systematic model errors and the radiative forcing show that generally the errors are not canceling out when the changes are computed. Therefore, reliable regional cli- mate changes can only be achieved after model improvements which reduce their systematic errors sufficiently. Also in future RCM experiments sujiciently long time-slices must be used in order to obtain statistically sign ijicant climate changes on the sub-continental scale aimed at with the present regionalization technique

Low-Energy Effective Theory, Unitarity, and Non-Decoupling Behavior in a Model with Heavy Higgs-Triplet Fields

We discuss the properties of a model incorporating both a scalar electroweak Higgs doublet and an electroweak Higgs triplet. We construct the low-energy effective theory for the light Higgs-doublet in the limit of small (but nonzero) deviations in the rho parameter from one, a limit in which the triplet states become heavy. For small deviations in the rho parameter from one, perturbative unitarity of WW scattering breaks down at a scale inversely proportional to the renormalized vacuum expectation value of the triplet field (or, equivalently, inversely proportional to the square-root of the deviation of the rho parameter from one). This result imposes an upper limit on the mass-scale of the heavy triplet bosons in a perturbative theory; we show that this upper bound is consistent with dimensional analysis in the low-energy effective theory. Recent articles have shown that the triplet bosons do not decouple, in the sense that deviations in the rho parameter from one do not necessarily vanish at one-loop in the limit of large triplet mass. We clarify that, despite the non-decoupling behavior of the Higgs-triplet, this model does not violate the decoupling theorem since it incorporates a large dimensionful coupling. Nonetheless, we show that if the triplet-Higgs boson masses are of order the GUT scale, perturbative consistency of the theory requires the (properly renormalized) Higgs-triplet vacuum expectation value to be so small as to be irrelevant for electroweak phenomenology.Comment: Revtex, 11 pages, 7 eps figures included; references updated and three footnotes adde

Hawking Radiation in the Dilaton Gravity with a Non-Minimally Coupled Scalar Field

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with the gravity is given, besides the minimal one, through an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a diferent motivation. The modification to the Hawking radiation is calculated explicity and shows an additional term that introduces a dependence on the (effective) mass of the black-hole.Comment: 13 pages, latex file, no figures, to be published in IJM