Generalized modified gravity with the second order acceleration equation

In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which have the acceleration equation of second order derivative. Then both the cosmic evolution and the weak-field limit of the theories are easily investigated. We find that not only the Big-bang singularity problem but also the current cosmic acceleration problem could be easily dealt with.Comment: 8 pages, 2 figures. To appear in Phys. Rev.

Continuous thickening of non-ideal suspensions

The purpose of this study was to investigate the steady state continuous thickening of non-ideal suspensions such as sludges from water and wastewater treatment plants. Suspensions of high grade calcium carbonate, activated sludges, water softening sludges, and suspensions of fine glass beads were used. The suspensions were thickened in a closed, continuous, pi lot, thickening system. The sol ids flux theory was used successfully for predicting performance of the steady state continuous thickener from batch settling velocities of the suspensions. For the optimal performance of the thickener, effective stirring of concentration layers near the underflow level was found to be an absolute necessity. This was to prevent dilute solids from reaching the thickener bottom. Homogeneous distribution of the feed over the area of the tank was also essential. The feed concentration generally did not affect the thickening function. However, the interaction between thickening and clarification functions of the tank was established through the magnitude of feed concentrations. As the feed concentration decreased with fixed solids loading, the overflow velocity increased, and the clarity of overflow generally deteriorated.U.S. Department of the InteriorU.S. Geological SurveyOpe

Graviton Mass or Cosmological Constant?

To describe a massive graviton in 4D Minkowski space-time one introduces a quadratic term in the Lagrangian. This term, however, can lead to a readjustment or instability of the background instead of describing a massive graviton on flat space. We show that for all local Lorentz-invariant mass terms Minkowski space is unstable. We start with the Pauli-Fierz (PF) term that is the only local mass term with no ghosts in the linearized approximation. We show that nonlinear completions of the PF Lagrangian give rise to instability of Minkowski space. We continue with the mass terms that are not of a PF type. Although these models are known to have ghosts in the linearized approximations, nonlinear interactions can lead to background change due to which the ghosts are eliminated. In the latter case, however, the graviton perturbations on the new background are not massive. We argue that a consistent theory of a massive graviton on flat space can be formulated in theories with extra dimensions. They require an infinite number of fields or non-local description from a 4D point of view.Comment: 16 pages; references and comments adde

Gravity induced over a smooth soliton

I consider gravity induced over a smooth (finite thickness) soliton. Graviton kinetic term is coupled to bulk scalar that develops solitonic vacuum expectation value. Couplings of Kaluza-Klein modes to soliton-localized matter are suppressed, giving rise to crossover distance $r_c=M_{P}^2/M_{*}^3$ between 4D and 5D behavior. This system can be viewed as a finite thickness brane regularization of the model of Dvali, Gabadadze and Porrati.Comment: 12 pages, 2 figure

Understanding mechanisms of genetic risk for adolescent internalizing and externalizing problems: The mediating role of parenting and personality

Genetic predispositions play an important role in the development of internalizing and externalizing behaviors. Understanding the mechanisms through which genetic risk unfolds to influence these developmental outcomes is critical for developing prevention and intervention efforts, capturing key elements of Irv's research agenda and scientific legacy. In this study, we examined the role of parenting and personality in mediating the effect of genetic risk on adolescents' major depressive disorder and conduct disorder symptoms. Longitudinal data were drawn from a sample of 709 European American adolescents and their mothers from the Collaborative Studies on Genetics of Alcoholism. Results from multivariate path analysis indicated that adolescents' depressive symptoms genome-wide polygenic scores (DS_GPS) predicted lower parental knowledge, which in turn was associated with more subsequent major depressive disorder and conduct disorder symptoms. Adolescents' DS_GPS also had indirect effects on these outcomes via personality, with a mediating effect via agreeableness but not via other dimensions of personality. Findings revealed that the pattern of associations was similar across adolescent gender. Our findings emphasize the important role of evocative gene-environment correlation processes and intermediate phenotypes in the pathways of risk from genetic predispositions to complex adolescent outcomes

Linearized Gravity in Isotropic Coordinates in the Brane World

We solve the Einstein equations in the Randall-Sundrum framework using an isotropic ansatz for the metric and obtain an exact expression to first order in the gravitational coupling. The solution is free from metric singularities away from the source and it satisfies the Israel matching condition on a straight brane. At distances far away from the source and on the physical brane this solution coincides with the 4-D Schwarzschild metric in isotropic coordinates. Furthermore we show that the extension of the standard Schwarzschild horizon in the bulk is tubular for any diagonal form of the metric while there is no restriction for the extension of the Schwarzschild horizon in isotropic coordinates.Comment: 13 pages, plain Te

Fragmentation pathways of nanofractal structures on surface

We present a detailed systematical theoretical analysis of the post-growth processes occurring in nanofractals grown on surface. For this study we developed a method which accounts for the internal dynamics of particles in a fractal. We demonstrate that particle diffusion and detachment controls the shape of the emerging stable islands on surface. We consider different scenarios of fractal post-growth relaxation and analyze the time evolution of the island's morphology. The results of our calculations are compared with available experimental observations, and experiments in which the post-growth relaxation of deposited nanostructures can be probed are suggested.Comment: 34 pages, 11 figure

String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras

The propagation differential for bosonic strings on a complex torus with three symmetric punctures is investigated. We study deformation aspects between two point and three point differentials as well as the behaviour of the corresponding Krichever-Novikov algebras. The structure constants are calculated and from this we derive a central extension of the Krichever-Novikov algebras by means of b-c systems. The defining cocycle for this central extension deforms to the well known Virasoro cocycle for certain kinds of degenerations of the torus. AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40Comment: 11 pages, amste

DGP Brane as a Gravity Conductor

We study how the DGP (Dvali-Gabadadze-Porrati) brane affects particle dynamics in linearized approximation. We find that once the particle is removed from the brane it is repelled to the bulk. Assuming that the cutoff for gravitational interaction is $M_*\sim 1/\epsilon$, we calculate the classical self energy of a particle as the function of its position. Since the particle wants to go to the region where its self energy is lower, it is repelled from the brane to the bulk where it gains its 5D self energy. Cases when mass of the particle $m8\pi^2M_*$ are qualitatively different, and in later case one has to take into account effects of strong gravity. In both cases the particle is repelled from the brane. For $m<8\pi^2M_*$ we obtain the same result from the 'electrostatic' analog of the theory. In that language mass (charge) in the bulk induces charge distribution on the brane which shields the other side of the brane and provides repulsive force. The DGP brane acts as a conducting plane in electrostatics (keeping in mind that in gravity different charges repel). The repulsive nature of the brane requires a certain localization mechanism. When the particle overcomes the localizing potential it rapidly moves to the bulk. Particles of mass $m>8\pi^2M_*$ form a black hole within $1/M_*$ distance from the brane.Comment: 13 pages, 3 figure