Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Relaxation of certain integral functionals depending on strain and chemical composition
2012
We provide a relaxation result in $BV \times L^q$, $1\leq q < +\infty$ as a first step towards the analysis of thermochemical equilibria.
Coupled systems of non-smooth differential equations
2012
Abstract We study the geometric qualitative behavior of a class of discontinuous vector fields in four dimensions. Explicit existence conditions of one-parameter families of periodic orbits for models involving two coupled relay systems are given. We derive existence conditions of one-parameter families of periodic solutions of systems of two second order non-smooth differential equations. We also study the persistence of such periodic orbits in the case of analytic perturbations of our relay systems. These results can be seen as analogous to the Lyapunov Centre Theorem.
A Positive Definite Advection Scheme Obtained by Nonlinear Renormalization of the Advective Fluxes
1989
Abstract A new method is developed to obtain a conservative and positive definite advection scheme that produces only small numerical diffusion. Advective fluxes are computed utilizing the integrated flux form of Tremback et al. These fluxes are normalized and then limited by upper and lower values. The resulting advection equation is numerically solved by means of the usual upstream procedure. The proposed treatment is not restricted to the integrated flux form but may also be applied to other known advection algorithms which are formulated in terms of advective fluxes. Different numerical tests are presented illustrating that the proposed scheme strongly reduces numerical and diffusion an…
Beyond the triangle and uniqueness relations: non-zeta counterterms at large $N$ from positive knots
1997
Counterterms that are not reducible to ζn are generated by 3F2 hypergeometric series arising from diagrams for which triangle and uniqueness relations furnish insufficient data. Irreducible double sums, corresponding to the torus knots (4, 3) = 819 and (5, 3) = 10124, are found in anomalous dimensions at O(1/N 3) in the large-N limit, which we compute analytically up to terms of level 11, corresponding to 11 loops for 4-dimensional field theories and 12 loops for 2-dimensional theories. High-precision numerical results are obtained up to 24 loops and used in Pade resummations of e-expansions, which are compared with analytical results in 3 dimensions. The O(1/N 3) results entail knots gener…
Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data
2008
Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.
A simple method for measurement of mechanical power in jumping.
1983
A simple test for the measurement of mechanical power during a vertical rebound jump series has been devised. The test consists of measuring the flight time with a digital timer (+/- 0.001 s) and counting the number of jumps performed during a certain period of time (e.g., 15-60 s). Formulae for calculation of mechanical power from the measured parameters were derived. The relationship between this mechanical power and a modification of the Wingate test (r = 0.87, n = 12 males) and 60 m dash (r = 0.84, n = 12 males) were very close. The mechanical power in a 60 s jumping test demonstrated higher values (20 W X kgBW-1) than the power in a modified (60 s) Wingate test (7 W X kgBW-1) and a Mar…
An Empirical Mode Decomposition Approach to Assess the Strength of Heart Period-Systolic Arterial Pressure Variability Interactions.
2020
This work proposes an empirical mode decomposition (EMD) method to assess the strength of the interactions between heart period (HP) and systolic arterial pressure (SAP) variability. EMD was exploited to decompose the original series (OR) into its first, and fastest, intrinsic mode function (IMF1) and the residual (RES) computed by subtracting the IMF1 from OR. EMD procedure was applied to both HP and SAP variability series. Then, the cross correlation function (CCF) was computed over OR, IMF1 and RES series derived from HP and SAP variability in 13 healthy subjects (age 27±8 yrs, 5 males) at rest in supine position (REST) and during head-up tilt (TILT). The first CCF maximum at negative ti…
Domain walls and ising-BLOCH transitions in parametrically driven systems.
2002
Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.
Numerical Front Propagation Using Kinematical Conservation Laws
2011
We use the newly formulated three-dimensional (3-D) kinematical conservation laws (KCL) to study the propagation of a nonlinear wavefront in a polytropic gas in a uniform state at rest. The 3-D KCL forms an under-determined system of six conservation laws with three involutive constraints, to which we add the energy conservation equation of a weakly nonlinear ray theory. The resulting system of seven conservation laws is only weakly hyperbolic and therefore poses a real challenge in the numerical approximation. We implement a central finite volume scheme with a constrained transport technique for the numerical solution of the system of conservation laws. The results of a numerical experimen…
Adiabatic evolution for systems with infinitely many eigenvalue crossings
1998
International audience; We formulate an adiabatic theorem adapted to models that present an instantaneous eigenvalue experiencing an infinite number of crossings with the rest of the spectrum. We give an upper bound on the leading correction terms with respect to the adiabatic limit. The result requires only differentiability of the considered projector, and some geometric hypothesis on the local behavior of the eigenvalues at the crossings.