Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions
1991
for some x in [0, rr]. The guiding idea of this paper is to observe the changes in the stability behavior of the solutions if we perturb the autonomous problem intro- ducing a forcing term g. In [8] it was shown that iff and g are related by a boundedness condi- tion (see condition (* ) in Theorem 3.1) then there exists a stable solution of (1.1) “close” to each stable solution of (1.2). We want to call these stable solutions of (1.1)
On the Kneser property for reaction–diffusion equations in some unbounded domains with an -valued non-autonomous forcing term
2012
Abstract In this paper, we prove the Kneser property for a reaction–diffusion equation on an unbounded domain satisfying the Poincare inequality with an external force taking values in the space H − 1 . Using this property of solutions we check also the connectedness of the associated global pullback attractor. We study also similar properties for systems of reaction–diffusion equations in which the domain is the whole R N . Finally, the results are applied to a generalized logistic equation.
Lévy-type diffusion on one-dimensional directed Cantor graphs.
2009
L\'evy-type walks with correlated jumps, induced by the topology of the medium, are studied on a class of one-dimensional deterministic graphs built from generalized Cantor and Smith-Volterra-Cantor sets. The particle performs a standard random walk on the sets but is also allowed to move ballistically throughout the empty regions. Using scaling relations and the mapping onto the electric network problem, we obtain the exact values of the scaling exponents for the asymptotic return probability, the resistivity and the mean square displacement as a function of the topological parameters of the sets. Interestingly, the systems undergoes a transition from superdiffusive to diffusive behavior a…
FOUNDATIONS OF FRACTIONAL DYNAMICS
1995
Time flow in dynamical systems is reconsidered in the ultralong time limit. The ultralong time limit is a limit in which a discretized time flow is iterated infinitely often and the discretization time step is infinite. The new limit is used to study induced flows in ergodic theory, in particular for subsets of measure zero. Induced flows on subsets of measure zero require an infinite renormalization of time in the ultralong time limit. It is found that induced flows are given generically by stable convolution semigroups and not by the conventional translation groups. This could give new insight into the origin of macroscopic irreversibility. Moreover, the induced semigroups are generated …
Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach
2017
Abstract A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based f…
Frequency domain identification of the fractional Kelvin-Voigt’s parameters for viscoelastic materials
2019
Abstract In this work, a new innovative method is used to identify the parameters of fractional Kelvin-Voigt constitutive equation. These parameters are: the order of fractional derivation operator, 0 ≤ α ≤ 1, the coefficient of fractional derivation operator, CV, and the stiffness of the model, KV. A particular dynamic test setup is developed to capture the experimental data. Its outputs are time histories of the excitation and excited accelerations. The investigated specimen is a polymeric cubic silicone gel material known as α-gel. Two kinds of experimental excitations are used as random frequencies and constant frequency harmonic excitations. In this study, experimental frequency respon…
Extended fractional-order Jeffreys model of viscoelastic hydraulic cylinder
2020
A novel modeling approach for viscoelastic hydraulic cylinders, with negligible inertial forces, is proposed, based on the extended fractional-order Jeffreys model. Analysis and physical reasoning for the parameter constraints and order of the fractional derivatives are provided. Comparison between the measured and computed frequency response functions and time domain transient response argues in favor of the proposed four-parameter fractional-order model.
Optimum pulse shape for minimum spectral occupancy in FSK signals
1984
The characteristics of a frequency shift keying (FSK) signal giving rise to maximum power within a prescribed frequency band are determined. The baseband pulse shape extends over any integer number of bit periods. An integral equation for the optimum pulse shape is derived and some simple properties of the solution are investigated. The equation has been solved for some values of the product of the prescribed band times the pulse duration and the signal shape is shown. Our results for the particular case of pulses only one bit period long are presented for purpose of comparison with results known in the literature. Plots of out-of-band power for some values of the prescribed band and of pul…
Large Eddy Simulations of Rough Turbulent Channel Flows Bounded by Irregular Roughness: Advances Toward a Universal Roughness Correlation
2020
The downward shift of the mean velocity profile in the logarithmic region, known as roughness function, $$\Delta U^+$$ , is the major macroscopic effect of roughness in wall bounded flows. This speed decrease, which is strictly linked to the friction Reynolds number and the geometrical properties which define the roughness pattern such as roughness height, density, shape parameters, has been deeply investigated in the past decades. Among the geometrical parameters, the effective slope (ES) seems to be suitable to estimate the roughness function at fixed friction Reynolds number, Re $$_{\tau }$$ . In the present work, the effects of several geometrical parameters on the roughness function, i…
On the properties of the radiosity equation near corners
2003
The radiosity equation is an integral equation of the second kind which describes the energy exchange by radiation between surfaces in R3. It is assumed that all surfaces are Lambertian reflectors and that all emitters are diffusive emitters. The radiosity equation plays an important role for the calculation of photo realistic images with the help of computers. Many surfaces which are used in practical calculations are only piecewise smooth and contain edges or corners. In this contribution we present regularity results for the solution of the radiosity equation in the vicinity of corners. The space of piecewise continuous functions is not suitable for this equation and we construct a new f…