Search results for "Mathematica"

Density flow over networks: A mean-field game theoretic approach

2014

A distributed routing control algorithm for dynamic networks has recently been presented in the literature. The networks were modeled using time evolution of density at network edges and the routing control algorithm allowed edge density to converge to a Wardrop equilibrium, which was characterized by an equal traffic density on all used paths. We borrow the idea and rearrange the density model to recast the problem within the framework of mean-field games. The contribution of this paper is three-fold. First, we provide a mean-field game formulation of the problem at hand. Second, we illustrate an extended state space solution approach. Third, we study the stochastic case where the density …

Assortment, but not knowledge of assortment, affects cooperation and individual success in human groups

2017

The success or failure of human collective action often depends on the cooperation tendencies of individuals in groups, and on the information that individuals have about each other's cooperativeness. However, it is unclear whether these two factors have an interactive effect on cooperation dynamics. Using a decision-making experiment, we confirm that groups comprising individuals with higher cooperation tendencies cooperate at a higher level than groups comprising individuals with low cooperation tendencies. Moreover, assorting individuals with similar cooperation tendency together affected behaviour so that the most cooperative individuals tended to cooperate more and the least cooperativ…

Multiple positive normalized solutions for nonlinear Schrödinger systems

2018

We consider the existence of multiple positive solutions to the nonlinear Schr\"odinger systems sets on $H^1(\mathbb{R}^N) \times H^1(\mathbb{R}^N)$, \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1 |u_1|^{r_1-2} u_1|u_2|^{r_2}, -\Delta u_2 &= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 + \beta r_2 |u_1|^{r_1} |u_2|^{r_2 -2} u_2, \end{aligned} \right. \] under the constraint \[ \int_{\mathbb{R}^N}|u_1|^2 \, dx = a_1,\quad \int_{\mathbb{R}^N}|u_2|^2 \, dx = a_2. \] Here $a_1, a_2 >0$ are prescribed, $\mu_1, \mu_2, \beta>0$, and the frequencies $\lambda_1, \lambda_2$ are unknown and will appear as Lagrange multipliers. Two cases are studied, the first …

Pants complex, TQFT and hyperbolic geometry

2021

We present a coarse perspective on relations of the $SU(2)$-Witten-Reshetikhin-Turaev TQFT, the Weil-Petersson geometry of the Teichm\"uller space, and volumes of hyperbolic 3-manifolds. Using data from the asymptotic expansions of the curve operators in the skein theoretic version of the $SU(2)$-TQFT, as developed by Blanchet, Habegger, Masbaum and Vogel, we define the quantum intersection number between pants decompositions of a closed surface. We show that the quantum intersection number admits two sided bounds in terms of the geometric intersection number and we use it to obtain a metric on the pants graph of surfaces. Using work of Brock we show that the pants graph equipped with this …

Directionlets: Anisotropic Multidirectional representation with separable filtering

2006

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based pe…

Gestalt/Gestalt Theory

2020

Gestalt is a concept introduced to solve the problems of unity, connection and order that objects manifest in experience. Philosophers trained at Franz Brentano’s teaching began to work on it to address epistemological and ontological questions about perception, cognition and the structure of objects. This work was seminal for Gestalt psychology, from the research of the Graz and Berlin Schools, carried on by Cesare Musatti, Fabio Metelli, Gaetano Kanizsa, Paolo Bozzi in Padua and Trieste, Albert Michotte and Paul Fraisse in Louvain, to that of Edgar Rubin and David Katz, but also of Karl Buhler, Egon Brunswik and Ludwig Kardos in Wien. Common is the tenet that the world looks as neither a …

Up-wind difference approximation and singularity formation for a slow erosion model

2020

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.

New sustainable technologies for buildings: the use of green roofs

2009

Balance equations-based properties of the Rabi Hamiltonian

2014

A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.

Quantum and classical dynamics of heavy quarks in a quark-gluon plasma

2018

We derive equations for the time evolution of the reduced density matrix of a collection of heavy quarks and antiquarks immersed in a quark gluon plasma. These equations, in their original form, rely on two approximations: the weak coupling between the heavy quarks and the plasma, the fast response of the plasma to the perturbation caused by the heavy quarks. An additional semi-classical approximation is performed. This allows us to recover results previously obtained for the abelian plasma using the influence functional formalism. In the case of QCD, specific features of the color dynamics make the implementation of the semi-classical approximation more involved. We explore two approximate…