Modeling carbon black reinforcement in rubber compounds

One of the advocated reinforcement mechanisms is the formation by the filler of a network interpenetrating the polymer network. The deformation and reformation of the filler network allows the explanation of low strain dynamic physical properties of the composite. The present model relies on a statistical study of a collection of elementary mechanical systems, This leads to a mathematical approach of the complex modulus G* = G' + iG". The storage and loss modulus (G' and G", respectively), are expressed in the form of two integrals capable of modeling their Variation with respect to strain

A Contractual Approach to Investor-State Regulatory Disputes

International investment arbitral tribunals are increasingly tasked with resolving regulatory disputes. This relatively new form of dispute involves a challenge by a foreign investor to a host state’s generally applicable regulation, enacted in good faith to promote the public interest but resulting incidentally in harm to the investor’s business. Such claims typically invoke the “fair and equitable treatment” standard provided for in the bilateral investment treaty between the host state and the investor’s home state. The dominant view among commentators, and increasingly among the tribunals themselves, is that regulatory disputes should be analyzed within a public law framework, using tools derived from constitutional or administrative law. That means, for example, balancing the investor’s rights and host state’s regulatory concerns as part of a proportionality analysis. I argue that the public law approach is flawed because it requires tribunals to weigh incommensurable values and ultimately to make policy judgments when they lack the expertise and legitimacy to do so. This Article proposes that tribunals instead draw on tools from contract law and theory to approximate what the contracting states intended when they agreed to a fair and equitable treatment standard. The investment treaties themselves give no guidance on how that standard should be applied to regulatory disputes. When courts confront similar gaps in contracts, they do not simply abandon the inquiry into the parties’ intent but instead apply additional tools or principles to form the best possible estimate. The Article explores three specific tools: a default rule approach and two default standards derived from contract law’s analysis of changed circumstances. More generally, I argue that a contractual approach, by focusing tribunals on the contracting states’ intent rather than requiring them to independently assess the substance of a host state’s policy, will facilitate more principled reasoning as well as enhance the tribunals’ legitimacy, and thereby better promote the goals of international investment in the long run

Applying Magnetized Accretion-Ejection Models to Microquasars: a preliminary step

We present in this proceeding some aspects of a model that should explain the spectral state changes observed in microquasars. In this model, ejection is assumed to take place only in the innermost disc region where a large scale magnetic field is anchored. Then, in opposite to conventional ADAF models, the accretion energy can be efficiently converted in ejection and not advected inside the horizon. We propose that changes of the disc physical state (e.g. transition from optically thick to optically thin states) can strongly modify the magnetic accretion-ejection structure resulting in the spectral variability. After a short description of our scenario, we give some details concerning the dynamically self-consistent magnetized accretion-ejection model used in our computation. We also present some preliminary results of spectral energy distribution.Comment: Proceeding of the fith Microquasar Workshop, June 7 - 13, 2004, Beijing, China. Accepted for publication in the Chinese Journal of Astronomy and Astrophysic

Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Universal fluctuations in subdiffusive transport

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW

Roughness Signature of Tribological Contact Calculated by a New Method of Peaks Curvature Radius Estimation on Fractal Surfaces

This paper proposes a new method of roughness peaks curvature radii calculation and its application to tribological contact analysis as characteristic signature of tribological contact. This method is introduced via the classical approach of the calculation of radius of asperity. In fact, the proposed approach provides a generalization to fractal profiles of the Nowicki's method [Nowicki B. Wear Vol.102, p.161-176, 1985] by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the studied profile. It is then established the increasing of the dispersion of the measures of that lines with that of the corresponding radii and the dependence of calculated radii on the fractal dimension of the studied curve. Consequently, the notion of peak is mathematically reformulated. The efficiency of the proposed method was tested via simulations of fractal curves such as those described by Brownian motions. A new fractal function allowing the modelling of a large number of physical phenomena was also introduced, and one of the great applications developed in this paper consists in detecting the scale on which the measurement system introduces a smoothing artifact on the data measurement. New methodology is applied to analysis of tribological contact in metal forming process

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field

Constructive Dimension and Turing Degrees

This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) / dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0, then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness extractor* that increases the algorithmic randomness of S, as measured by constructive dimension. A number of applications of this result shed new light on the constructive dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previously-known zero-one law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) = dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive Hausdorff and packing dimension equal to 1. Finally, it is shown that no single Turing reduction can be a universal constructive Hausdorff dimension extractor, and that bounded Turing reductions cannot extract constructive Hausdorff dimension. We also exhibit sequences on which weak truth-table and bounded Turing reductions differ in their ability to extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems, 45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to insufficient care with the choice of delta. This version modifies that proof to fix the error

Level Sets of the Takagi Function: Local Level Sets

The Takagi function \tau : [0, 1] \to [0, 1] is a continuous non-differentiable function constructed by Takagi in 1903. The level sets L(y) = {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a notion of local level set into which level sets are partitioned. Local level sets are simple to analyze, reducing questions to understanding the relation of level sets to local level sets, which is more complicated. It is known that for a "generic" full Lebesgue measure set of ordinates y, the level sets are finite sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas x, the level set L(\tau(x)) is uncountable. An interesting singular monotone function is constructed, associated to local level sets, and is used to show the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation numbering. The final publication will soon be available at springerlink.co