Related papers: Linear theory and velocity correlations of cluster…
We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We…
Special relativity includes a concealed mechanism for reducing time-dilation effects in two mutually-receding objects. Forwarding their signals via one or more intermediate physical relay stages (a "probe chain") allows enhanced…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…
We present a novel derivation of the elastic theory of shells. We use the language of Geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools…
The parallel linear transports defined by flat linear connection are axiomatically described. On this basis a number of properties, some of which are new, of these transports and connections are derived.
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
Recently, the first author proposed a measure to calculate Pearson correlations for node values expressed in a network, by taking into account distances or metrics defined on the network. In this technical note, we show that using an…
We investigate the feasibility of carrying out likelihood analysis on the velocities of galaxy clusters to determine power spectrum parameters. Using N-body simulations of cosmological density fields we show that the velocity field traced…
Superclusters are a convenient way to partition and characterize the large scale structure of the Universe. In this Letter we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply…
With recent advances in sensing and tracking technology, trajectory data is becoming increasingly pervasive and analysis of trajectory data is becoming exceedingly important. A fundamental problem in analyzing trajectory data is that of…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a…
Deviations between the form of trajectory assumed in a fit to a set of measurements and the actual form of the trajectory can give rise to sequential correlations in the residuals from the fit. These correlations can provide a more powerful…
Recently, it has been shown that the causality and information flow between two time series can be inferred in a rigorous and quantitative sense, and, besides, the resulting causality can be normalized. A corollary that follows is, in the…
This paper examines several methods of tracing galaxies in N-body simulations and their effects on the derived galaxy statistics, especially measurements of velocity bias. Using two simulations with identical initial conditions, one…
Linear lattice gauge theory is based on link variables that are arbitrary complex or real $N\times N$ matrices, in distinction to the usual (non-linear) formulation with unitary or orthogonal matrices. For a large region in parameter space…