MOND as the weak-field limit of an extended metric theory of gravity

We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity.Comment: To appear in the proceedings of the 2011 Spanish Relativity Meeting (ERE2011) held in Madrid, Spain, 4 page

Phase II of the ASCE Benchmark Study on SHM

The task group on structural health monitoring of the Dynamic Committee of ASCE was formed in 1999 at the 12 th Engineering Mechanics Conference. The task group has designed a number of analytical studies on a benchmark structure and there are plans to follow these with an experimental program. The first phase of the analytical studies was completed in 2001. The second phase, initiated in the summer of 2001, was formulated in the light of the experience gained on phase I and focuses on increasing realism in the simulation of the discrepancies between the actual structure and the mathematical model used in the analysis. This paper describes the rational that lead the SHM task group to the definition of phase II and presents the details of the cases that are being considered

Non-relativistic Extended Gravity and its applications across different astrophysical scales

Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to Newton's gravity and to a MOND-like description in two different mass and length regimes. It is shown that a modification on the force sector (and not in the dynamical one as MOND does) is more convenient and can reproduce and predict different phenomena usually ascribed to dark matter at the non-relativistic level.Comment: 4 pages, 2 figures. To appear in the proceedings of the 2011 Spanish Relativity Meeting (ERE2011) held in Madrid, Spai

Interference pattern in the collision of structures in the BEC dark matter model: comparison with fluids

In order to explore nonlinear effects on the distribution of matter during collisions within the Bose-Einstein condensate (BEC) dark matter model driven by the Schr\"odinger-Poisson system of equations, we study the head-on collision of structures and focus on the interference pattern formation in the density of matter during the collision process. We explore the possibility that the collision of two structures of fluid matter modeled with an ideal gas equation of state also forms interference patterns and found a negative result. Given that a fluid is the most common flavor of dark matter models, we conclude that one fingerprint of the BEC dark matter model is the pattern formation in the density during a collision of structures.Comment: 7 pages, 22 eps figure

Modelling the inorganic nitrogen behaviour in a small Mediterranean forested catchment, Fuirosos (Catalonia)

The aim of this work was to couple a nitrogen (N) sub-model to already existent hydrological lumped (LU4-N) and semi-distributed (LU4-R-N and SD4-R-N) conceptual models, to improve our understanding of the factors and processes controlling nitrogen cycling and losses in Mediterranean catchments. The N model adopted provides a simplified conceptualization of the soil nitrogen cycle considering mineralization, nitrification, immobilization, denitrification, plant uptake, and ammonium adsorption/desorption. It also includes nitrification and denitrification in the shallow perched aquifer. We included a soil moisture threshold for all the considered soil biological processes. The results suggested that all the nitrogen processes were highly influenced by the rain episodes and that soil microbial processes occurred in pulses stimulated by soil moisture increasing after rain. Our simulation highlighted the riparian zone as a possible source of nitrate, especially after the summer drought period, but it can also act as an important sink of nitrate due to denitrification, in particular during the wettest period of the year. The riparian zone was a key element to simulate the catchment nitrate behaviour. The lumped LU4-N model (which does not include the riparian zone) could not be validated, while both the semi-distributed LU4-R-N and SD4-R-N model (which include the riparian zone) gave satisfactory results for the calibration process and acceptable results for the temporal validation process

Effect of processing conditions on the thermal and electrical conductivity of poly (butylene terephthalate) nanocomposites prepared via ring-opening polymerization

Successful preparation of polymer nanocomposites, exploiting graphene-related materials, via melt mixing technology requires precise design, optimization and control of processing. In the present work, the effect of different processing parameters during the preparation of poly (butylene terephthalate) nanocomposites, through ring-opening polymerization of cyclic butylene terephthalate in presence of graphite nanoplatelets (GNP), was thoroughly addressed. Processing temperature (240{\deg}C or 260{\deg}C), extrusion time (5 or 10 minutes) and shear rate (50 or 100 rpm) were varied by means of a full factorial design of experiment approach, leading to the preparation of polybutylene terephthalate/GNP nanocomposite in 8 different processing conditions. Morphology and quality of GNP were investigated by means of electron microscopy, X-ray photoelectron spectroscopy, thermogravimetry and Raman spectroscopy. Molecular weight of the polymer matrix in nanocomposites and nanoflake dispersion were experimentally determined as a function of the different processing conditions. The effect of transformation parameters on electrical and thermal properties was studied by means of electrical and thermal conductivity measurement. Heat and charge transport performance evidenced a clear correlation with the dispersion and fragmentation of the GNP nanoflakes; in particular, gentle processing conditions (low shear rate, short mixing time) turned out to be the most favourable condition to obtain high conductivity values

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

Dimensional analysis and Rutherford Scattering

Dimensional analysis, and in particular the Buckingham $\Pi$ theorem is widely used in fluid mechanics. In this article we obtain an expression for the impact parameter from Buckingham's theorem and we compare our result with Rutherford's original discovery found in the early twentieth century

Dynamical Arrest in Attractive Colloids: The Effect of Long-Range Repulsion

We study gelation in suspensions of model colloidal particles with short-ranged attractive and long-ranged repulsive interactions by means of three-dimensional fluorescence confocal microscopy. At low packing fractions, particles form stable equilibrium clusters. Upon increasing the packing fraction the clusters grow in size and become increasingly anisotropic until finally associating into a fully connected network at gelation. We find a surprising order in the gel structure. Analysis of spatial and orientational correlations reveals that the gel is composed of dense chains of particles constructed from face-sharing tetrahedral clusters. Our findings imply that dynamical arrest occurs via cluster growth and association.Comment: Final version: Phys. Rev. Lett. 94, 208301 (2005