Indirect searches for dark matter

The current status of indirect searches for dark matter has been reviewed in a schematic way here. The main relevant experimental results of the recent years have been listed and the excitements and disappointments that their phenomenological interpretations in terms of almost-standard annihilating dark matter have brought along have been discussed. The main sources of uncertainties that affect this kind of searches are also listed. [Report number: Saclay T11/206, CERN-PH-TH/2011-257, extended version in arXiv:1202.1454], [Prepared for the Proceedings of Lepton?CPhoton 2011, Mumbai, India, 22?C27 Aug. 2011].     

Dihedral Branches Coverings of Hyperbolic Orbifolds

We consider the class of hyperbolic 3-orbifolds whose underlying topological space is the 3-sphere S ³ and whose singular set is a trivalent graph with singular index 2 along each edge (an important special case occurs when the trivalent graph is the 1-skeleton of a hyperbolic polyhedron). Our main result is a classification of the D-branched coverings of these orbifolds (where D₂ is the dihedral group of order 4) under some general conditions on their isometry groups or the lengths of their geodesics.     

Reorientational dynamics in a liquid organized system: Brillouin and depolarized Rayleigh scattering experiments in 1-octanol

Light scattering experiments, with dispersive and interferometric techniques, have been performed to study the orientational relaxation dynamics in 1-octanol, a structured liquid system having quite long living H-bonded clusters. Different temporal windows have been opened with these experiments to investigate the temporal events connected to the orientational relaxation dynamics of this molecular liquid. The present results have been compared with previous Monte Carlo MD simulations and experimental dielectric relaxation functions. They show that in the high frequency domain two additional very fast processes can be detected which have not been revealed by dielectric function relaxation.     

In vivo SPECTROPHOTOMETRIC EVALUATION OF NEOPLASTIC AND NON-NEOPLASTIC SKIN PIGMENTED LESIONS–I. REFLECTANCE MEASUREMENTS

Reflectance spectrophotometry from 400 to 800 nm on different cutaneous pigmented lesions, including primary and metastatic malignant melanoma, pigmented nevi, lentigo and seborrhoeic keratosis, has been performed by using an external integrating sphere coupled to a spectrophotometer. Measurements show that reflectance spectra of the different lesions manifest dissimilar patterns, particularly in the near IR region. Comparison of reflectance of nevi with that of malignant melanomas results in a highly significant difference (P less than 10(-6)) between the two samples. Though interpretation of the spectra remains difficult as a result of the complexity of the optical processes of scattering and absorption, our results suggest that a detailed analysis of the reflectance spectrum may give clinically useful information, and could be utilized as an aid in clinical diagnosis of cutaneous pigmented lesions, especially where malignant melanoma is concerned.     

A MIXED CONTROL PROBLEM OF THE MANAGEMENT OF NATURAL RESOURCES

In this paper, we study the optimal solutions of a model of natural resource management which allows for both impulse and continuous harvesting policies. This type of model is known in the literature as mixed optimal control problem. In the resource management context, each type of control represents a different harvesting technology, which has a different cost. In particular, we want to know when the following conjecture made by Clark is an optimal solution to this mixed optimal control problem: if the harvesting capacity is unlimited, it is optimal to jump immediately to the steady state of the continuous time problem and then to stay there. We show that under a particular relationship between the continuous and the impulse profit function, the conjecture made by Clark is true. In other cases, however, it is either better to use only continuous control variables or to jump to resource levels which are smaller than the steady state and then let the resource grow back to the steady state. These results emphasize the importance of the cost functions in the modeling of natural resource management.     

The free energy of a reaction coordinate at multiple constraints: a concise formulation

The free energy as a function of the reaction coordinate (rc) is the key quantity for the computation of equilibrium and kinetic quantities. When it is considered as the potential of mean force, the problem is the calculation of the mean force for given values of the rc. We reinvestigate the PMCF (potential of mean constraint force) method which applies a constraint to the rc to compute the mean force as the mean negative constraint force and a metric tensor correction. The latter allows for the constraint imposed to the rc and possible artefacts due to multiple constraints of other variables which for practical reasons are often used in numerical simulations. Two main results are obtained that are of theoretical and practical interest. First, the correction term is given a very concise and simple shape which facilitates its interpretation and evaluation. Secondly, a theorem describes various rcs and possible combinations with constraints that can be used without introducing any correction to the constraint force. The results facilitate the computation of free energy by molecular dynamics simulations.     

Free Vibrations of Cylindrical Shells with Non-Axisymmetric Mass Distribution on Elastic Bed

The free vibrations of circular cylindrical shells partiallyloaded by a distributed mass and rested on an elastic bed are studied in this paper. Both the mass-load and the elastic bed are assumed to be applied on limited arcs and with arbitrary distributions in circumferential direction,while they are considered to be uniformly distributed in longitudinaldirection on the entire shell length. Therefore, the problem is notaxisymmetric. The solution is obtained by using the development of theflexural mode shapes in a Fourier series, whose coefficients are determinedby rendering the Rayleigh quotient stationary, so a Galerkin equation isobtained. The proposed method is independent of the boundary conditionsat the shell ends. The results are satisfactorily compared to FEM results.Finally, the influence of the mass-load and of the bed stiffness on thenatural frequencies and mode shapes of a simply supported shell is shownand discussed.     

Oscillation theory and numerical solution of fourth-order Sturm--Liouville problems

A shooting method is developed to approximate the eigenvaluesand eigenfunc-tions of a fourth-order Sturm-Liouville problem.The main tool is a miss-distance function M(), which countsthe number of eigenvalues less than A. The method approximatesthe coefficients of the differential equation by piecewise-constantfunctions, which enables an exact solution to be found on eachmesh interval. In order to calculate N() for the approximateproblem, certain oscillation numbers N_L and N_R must be computed.These consist of sums of nullities (or rank deficiencies) of2 x 2 matrices obtained from the solutions of the approximatedifferential equation. Although these solutions can be foundexplicitly, the calculation of N_L and N_R is non-trivial, andis obtained by using certain properties of M().     

Comparison of Random Cash Flows

In this paper we provide stochastic-dominance conditions forrandom cumulated cash flows, when various criteria of choiceare assumed. Three (progressively finer) criteria are considered.The first one assumes only the expected utility principle. Thesecond one involves discounting and preference scaling. Thethird one involves discounting and preference scaling, too,but in reverse order. Our results are finally compared withother known results for the case of nonrandom cash flows.