281 research outputs found
Eigenvalue density of empirical covariance matrix for correlated samples
We describe a method to determine the eigenvalue density of empirical
covariance matrix in the presence of correlations between samples. This is a
straightforward generalization of the method developed earlier by the authors
for uncorrelated samples. The method allows for exact determination of the
experimental spectrum for a given covariance matrix and given correlations
between samples in the limit of large N and N/T=r=const with N being the number
of degrees of freedom and T being the number of samples. We discuss the effect
of correlations on several examples.Comment: 12 pages, 5 figures, to appear in Acta Phys. Pol. B (Proceedings of
the conference on `Applications of Random Matrix Theory to Economy and Other
Complex Systems', May 25-28, 2005, Cracow, Polan
Pair-factorized steady states on arbitrary graphs
Stochastic mass transport models are usually described by specifying hopping
rates of particles between sites of a given lattice, and the goal is to predict
the existence and properties of the steady state. Here we ask the reverse
question: given a stationary state that factorizes over links (pairs of sites)
of an arbitrary connected graph, what are possible hopping rates that converge
to this state? We define a class of hopping functions which lead to the same
steady state and guarantee current conservation but may differ by the induced
current strength. For the special case of anisotropic hopping in two dimensions
we discuss some aspects of the phase structure. We also show how this case can
be traced back to an effective zero-range process in one dimension which is
solvable for a large class of hopping functions.Comment: IOP style, 9 pages, 1 figur
Quantum widening of CDT universe
The physical phase of Causal Dynamical Triangulations (CDT) is known to be
described by an effective, one-dimensional action in which three-volumes of the
underlying foliation of the full CDT play a role of the sole degrees of
freedom. Here we map this effective description onto a statistical-physics
model of particles distributed on 1d lattice, with site occupation numbers
corresponding to the three-volumes. We identify the emergence of the quantum
de-Sitter universe observed in CDT with the condensation transition known from
similar statistical models. Our model correctly reproduces the shape of the
quantum universe and allows us to analytically determine quantum corrections to
the size of the universe. We also investigate the phase structure of the model
and show that it reproduces all three phases observed in computer simulations
of CDT. In addition, we predict that two other phases may exists, depending on
the exact form of the discretised effective action and boundary conditions. We
calculate various quantities such as the distribution of three-volumes in our
model and discuss how they can be compared with CDT.Comment: 19 pages, 13 figure
Comparison of numerical and experimental strains distributions in composite panel for aerospace applications
In structural applications of aerospace industry, weight efficiency, understood as minimal weight and maximal stiffness, is of great importance. This criterion can be achieved by composite lightweight structures. Typical structures for aforementioned applications are sandwich panels (e.g., with honeycomb core) and stiffened panels (e.g., with blade ribs, T-bar ribs, or hat ribs). In this paper, a hat-stiffened panel, made of carbon/epoxy woven composite, is considered. Results of experiments, consisting of loading the panel and measuring exciting forces and strains (using strain gages), are presented. The results are compared to strains distribution
obtained from finite element model of the panel.The research was partially funded from financial resources from the statutory subsidy of the
Faculty of Mechanical Engineering, Silesian University of Technology, in 2021.
W.M. acknowledges the National Agency for Academic Exchange of Poland (under the Academic International Partnerships program, grant agreement PPI/APM/2018/1/00004) for supporting training in the University of Minho, which enabled execution of the study
Mass condensation on networks
We construct classical stochastic mass transport processes for stationary states which are chosen to factorize over pairs of sites of an undirected, connected, but otherwise arbitrary graph. For the special topology of a ring we derive static properties such as the critical point of the transition between the liquid and the condensed phase, the shape of the condensate and its scaling with the system size. It turns out that the shape is not universal, but determined by the interplay of local and ultralocal interactions. In two dimensions the effect of anisotropic interactions of hopping rates can be treated analytically, since the partition function allows a dimensional reduction to an effective one-dimensional zero-range process. Here we predict the onset, shape and scaling of the condensate on a square lattice. We indicate further extensions in the outlook
Measurements of polarimetric sensitivity to hydrostatic pressure, strain and temperature in birefringent dual-core microstructured polymer fiber
We experimentally characterized a birefringent microstructured polymer fiber of specific construction, which allows for single mode propagation in two cores separated by a pair of large holes. The fiber exhibits high birefringence in each of the cores as well as relatively weak coupling between the cores. Spectral dependence of the group and the phase modal birefringence was measured using an interferometric method. We have also measured the sensing characteristics of the fiber such as polarimetric sensitivity to hydrostatic pressure, strain and temperature. Moreover, we have studied the effect of hydrostatic pressure and strain on coupling between the cores
Predictable Properties of Fitness Landscapes Induced by Adaptational Tradeoffs
Fitness effects of mutations depend on environmental parameters. For example, mutations that increase fitness of bacteria at high antibiotic concentration often decrease fitness in the absence of antibiotic, exemplifying a tradeoff between adaptation to environmental extremes. We develop a mathematical model for fitness landscapes generated by such tradeoffs, based on experiments that determine the antibiotic dose-response curves of Escherichia coli strains, and previous observations on antibiotic resistance mutations. Our model generates a succession of landscapes with predictable properties as antibiotic concentration is varied. The landscape is nearly smooth at low and high concentrations, but the tradeoff induces a high ruggedness at intermediate antibiotic concentrations. Despite this high ruggedness, however, all the fitness maxima in the landscapes are evolutionarily accessible from the wild type. This implies that selection for antibiotic resistance in multiple mutational steps is relatively facile despite the complexity of the underlying landscape
Polarimetric sensitivity to hydrostatic pressure and temperature in birefringent dual-core microstructured polymer fiber
We experimentally characterized a birefringent microstructured polymer fiber of specific construction, which allows for single mode propagation in two cores separated by a pair of large holes. The fiber exhibits high birefringence in each of the cores as well as relatively weak coupling between the cores. Spectral dependence of the group and the phase modal birefringence was measured using an interferometric method. We have also measured the sensing characteristics of the fiber such as the polarimetric sensitivity to hydrostatic pressure and temperature
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