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We study the existence of singular separable solutions to a class of quasilinear equations with reaction term. In the 2-dim case, we use a dynamical system approach to construct our solutions.

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…

In this paper we study the construction of a discrete solution for a hyperbolic system of partial differentials of the strongly coupled type. In its construction, the discrete separation of matricial variable method was followed. Two…

We study the homogenization property of systems of quasi-linear PDEs of parabolic type with periodic coefficients, highly oscillating drift and highly oscillating nonlinear term. To this end, we propose a probabilistic approach based on the…

Real-time gas classification is an essential issue and challenge in applications such as food and beverage quality control, accident prevention in industrial environments, for instance. In recent years, the Deep Learning (DL) models have…

In this paper, a methodology to calculate the sensitivity of the least stable modes of fluid-structure interaction systems with respect to local forces is presented. We make use of the adjoint equations of the flow-structure coupled system…

This paper presents existence and uniqueness results for reflected system of quasilinear stochastic partial differential equations in a convex domain D from Rk. The method is based on the probabilistic interpretation of the solution by…

We present a sparse sensing framework based on Dynamic Mode Decomposition (DMD) to identify flow regimes and bifurcations in large-scale thermo-fluid systems. Motivated by real-time sensing and control of thermal-fluid flows in buildings…

This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…

Electro-hydraulic servo-systems are widely employed in industrial applications such as robotic manipulators, active suspensions, precision machine tools and aerospace systems. They provide many advantages over electric motors, including…

We consider the (complete) Euler system describing the motion of a compressible perfect fluid. We propose a platform suitable for constructing the statistical solutions. The main ingredients of our approach include: 1. The concept of…

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as…

We propose a control approach for a class of nonlinear mechanical systems to stabilize the system under study while ensuring that the oscillations of the transient response are reduced. The approach is twofold: (i) we apply our technique…

We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes-Elasticity system, with respect to the reference domain of the elastic structure immersed in a viscous fluid. The…

Dynamical systems can autonomously adapt their organization so that the required target dynamics is reproduced. In the previous Rapid Communication [Phys. Rev. E 90,030901(R) (2014)], it was shown how such systems can be designed using…

Rigid body dynamics algorithms play a crucial role in several components of a robot controller and simulations. Real time constraints in high frequency control loops and time requirements of specific applications demand these functions to…

Valveless pumping assists in fluid transport in various organisms and engineering systems. In a previous work, to study the actuator impact effects on valveless pumping, we constructed a piecewise-linear lumped-parameter model for a…

The normal form and zero dynamics are powerful tools useful in analysis and control of both linear and nonlinear systems. There are no simple closed form solutions to the general zero dynamics problem for nonlinear systems. A few algorithms…

We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…

Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and is rarely available in closed form. In this paper, we study…