arXiv subjects

C. D. Rodríguez-Camargo

Publications and source records attributed to C. D. Rodríguez-Camargo.

6 recordsLinked to original sources

arXiv2024

Consensus-based Distributed Optimization for Multi-agent Systems over Multiplex Networks

Multilayer networks provide a more comprehensive framework for exploring real-world and engineering systems than traditional single-layer networks, consisting of multiple interacting networks. However, despite significant research in distributed optimization for single-layer networks, similar progress for multilayer systems is lacking. This paper proposes two algorithms for distributed optimization problems in multiplex networks using the supra-Laplacian matrix and its diffusion dynamics. The algorithms include a distributed saddle-point algorithm and its variation as a distributed gradient descent algorithm. By relating consensus and diffusion dynamics, we obtain the multiplex supra-Laplacian matrix. We extend the distributed gradient descent algorithm for multiplex networks using this matrix and analyze the convergence of both algorithms with several theoretical results. Numerical examples validate our proposed algorithms, and we explore the impact of interlayer diffusion on consensus time. We also present a coordinated dispatch for interdependent infrastructure networks (energy-gas) to demonstrate the application of the proposed framework to real engineering problems.

math.OC↗

arXiv2024

The generalized second law in Euclidean Schwarzschild black hole

We discuss the Bekenstein generalized entropy of a Schwarzschild black hole, with the contribution of an external matter field affected by degrees of freedom near the event horizon. In the Euclidean section of the Schwarzschild manifold, we consider an Euclidean quantum effective model, a scalar theory in the presence of an additive disorder field. The average of the Gibbs free energy over the ensemble of possible configurations of the disorder is obtained by the distributional zeta-function method. In the series representation for the average free energy, the effective actions give rise to generalized Schrödinger operators on Riemannian manifolds. Finally, is presented the generalized entropy density with the contributions of the black hole geometric entropy and the external matter fields. The validity of the generalized second law using Euclidean functional methods is obtained.

gr-qc↗

arXiv2022

Repulsive to Attractive Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model

Critical fluctuations of some order parameter describing a fluid generates long-range forces between boundaries. Here, we discuss fluctuation-induced forces associated to a disordered Landau-Ginzburg model defined in a $d$-dimensional slab geometry $\mathbb R^{d-1}\times[0,L]$. In the model the strength of the disordered field is defined by a non-thermal control parameter. We study a nearly critical scenario, using the distributional zeta-function method, where the quenched free energy is written as a series of the moments of the partition function. In the Gaussian approximation, we show that, for each moment of the partition function, and for some specific strength of the disorder, the non-thermal fluctuations, associated to an order parameter-like quantity, becomes long-ranged. We demonstrate that the sign of the fluctuation induced force between boundaries, depend in a non-trivial way on the strength of the aforementioned non-thermal control parameter.

cond-mat.dis-nn↗

arXiv2021

The Sherrington-Kirkpatrick model for spin glasses: A new approach for the solution

We discuss the Sherrington-Kirkpatrick mean-field version of a spin glass within the distributional zeta-function method (DZFM). In the DZFM, since the dominant contribution to the average free energy is written as a series of moments of the partition function of the model, the spin-glass multivalley structure is obtained. Also, an exact expression for the saddle points corresponding to each valley and a global critical temperature showing the existence of many stables or at least metastables equilibrium states is presented. Near the critical point we obtain analytical expressions of the order parameters that are in agreement with phenomenological results. We evaluate the linear and nonlinear susceptibility and we find the expected singular behavior at the spin-glass critical temperature. Furthermore, we obtain a positive definite expression for the entropy and we show that ground-state entropy tends to zero as the temperature goes to zero. We show that our solution is stable for each term in the expansion. Finally, we analyze the behavior of the overlap distribution, where we find a general expression for each moment of the partition function.

cond-mat.dis-nn↗

arXiv2020

Systemic Performance Measures from Distributional Zeta-Function

We propose the use of the Distributional Zeta-Function (DZF) for constructing a new set of Systemic Performance Measures (SPM). SPM have been proposed to investigate network synthesis problems such as the growing of linear consensus networks. The adoption of the DZF has shown interesting physical consequences that in the usual replica method are still unclarified, i.e., the connection between the spontaneous symmetry breaking mechanism and the structure of the replica space in the disordered model. We relate topology of the network and the partition function present in the DZF by using the spectral and the Hamiltonian structure of the system. The studied objects are the generalized partition funcion, the DZF, the Expected value of the replica partition function, and the quenched free energy of a field network. We show that with these objects we need few operations to increase the percentage of performance enhancement of a network. Furthermore, we evalue the location of the optimal added links for each new SPM and calculate the performance improvement of the new network for each new SPM via the spectral zeta function, $\mathcal{H}_{2}$-norm, and the communicability between nodes. We present the advantages of this new set of SPM in the network synthesis and we propose other methods for using the DZF to explore some issues such as disorder, critical phenomena, finite-temperature, and finite-size effects on networks. Relevance of the results are discussed.

cond-mat.stat-mech↗

arXiv2018

Finite-time response function of uniformly accelerated entangled atoms

We examine the transition probability from the ground state to a final entangled state of a system of uniformly accelerated two-level atoms weakly coupled with a massless scalar field in Minkowski vacuum. Using time-dependent perturbation theory we evaluate the finite-time response function and we identify the mutual influence of atoms via the quantum field as a coherence agent in each response function terms. The associated thermal spectrum perceived by the atoms is found for a finite time interval. By considering modifications of specific parameters of our setup, we also analyze how the transition probabilities are affected by the smoothness of the switching of the atom-field coupling. In addition, we study the mean life of the symmetric maximally entangled state for different accelerations. Our calculations reveal that smooth switching is more efficient than sudden switching concerning the reduction of the decay of the entangled state. The possible relevance of our results is discussed.

quant-ph↗