Search results for "Vector field"
showing 10 items of 164 documents
Quasi-conformal mapping theorem and bifurcations
1998
LetH be a germ of holomorphic diffeomorphism at 0 ∈ ℂ. Using the existence theorem for quasi-conformal mappings, it is possible to prove that there exists a multivalued germS at 0, such thatS(ze 2πi )=H○S(z) (1). IfH λ is an unfolding of diffeomorphisms depending on λ ∈ (ℂ,0), withH 0=Id, one introduces its ideal $$\mathcal{I}_H$$ . It is the ideal generated by the germs of coefficients (a i (λ), 0) at 0 ∈ ℂ k , whereH λ(z)−z=Σa i (λ)z i . Then one can find a parameter solutionS λ (z) of (1) which has at each pointz 0 belonging to the domain of definition ofS 0, an expansion in seriesS λ(z)=z+Σb i (λ)(z−z 0) i with $$(b_i ,0) \in \mathcal{I}_H$$ , for alli. This result may be applied to the…
Stochastic differential equations with coefficients in Sobolev spaces
2010
We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth; for the drift coefficient $A_0$, we consider two cases: (i) $A_0$ is continuous whose distributional divergence $\delta(A_0)$ w.r.t. the Gaussian measure $\gamma_d$ exists, (ii) $A_0$ has the Sobolev regularity $W_\text{loc}^{1,p'}$ for some $p'>1$. Assume $\int_{\R^d} \exp\big[\lambda_0\bigl(|\delta(A_0)| + \sum_{j=1}^m (|\delta(A_j)|^2 +|\nabla A_j|^2)\bigr)\big] \d\gamma_d0$, in the case (i), if the pathwise uniqueness of solutions holds, then the push-f…
The electromagnetic and Proca fields revisited: A unified quantization
1997
Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μφ(x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U(1)(x, t), acquire dyn…
Highly efficient full-wave electromagnetic analysis of 3-D arbitrarily shaped waveguide microwave devices using an integral equation technique
2015
A novel technique for the full-wave analysis of 3-D complex waveguide devices is presented. This new formulation, based on the Boundary Integral-Resonant Mode Expansion (BI-RME) method, allows the rigorous full-wave electromagnetic characterization of 3-D arbitrarily shaped metallic structures making use of extremely low CPU resources (both time and memory). The unknown electric current density on the surface of the metallic elements is represented by means of Rao-Wilton-Glisson basis functions, and an algebraic procedure based on a singular value decomposition is applied to transform such functions into the classical solenoidal and nonsolenoidal basis functions needed by the original BI-RM…
Unit Vector Fields that are Critical Points of the Volume and of the Energy: Characterization and Examples
2007
In the last few years, many works have appeared containing examples and general results on harmonicity and minimality of vector fields in different geometrical situations. This survey will be devoted to describe many of the known examples, as well as the general results from where they are obtained.
An upper bound of the index of an equilibrium point in the plane
2012
Abstract We give an upper bound of the index of an isolated equilibrium point of a C 1 vector field in the plane. The vector field is decomposed in gradient and Hamiltonian components. This decomposition is related with the Loewner vector field. Associated to this decomposition we consider the set Π where the gradient and Hamiltonian components are linearly dependent. The number of branches of Π starting at the equilibrium point determines the upper bound of the index.
Desychronization of one-parameter families of stable vector fields
2005
Given a one-parameter family of vector fields on , Fλ(x), , such that for each λ, Fλ has a global asymptotically stable equilibrium point xλ, we construct a vector field on of the form G(λ, x) = (g(λ, x), Fλ(x)) which exhibits chaotic behaviour. This result is an incursion in the inverse problem of master–slave synchronization.This paper discusses self-disorganization of parameter dependent stable vector fields. Motivations are found in applications to drug design: one way to lead an unfriendly organism to death is to destabilize its metabolism. In this paper we envisage the mathematical aspect of the question. We show that for a very stable system (one globally attracting equilibrium state…
MAST solution of advection problems in irrotational flow fields
2007
Abstract A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the so…
Existence and uniqueness of solutions to superdifferential equations
1993
Abstract We state and prove the theorem of existence and uniqueness of solutions to ordinary superdifferential equations on supermanifolds. It is shown that any supervector field, X = X0 + X1, has a unique integral flow, Г: R 1¦1 x (M, AM) → (M, AM), satisfying a given initial condition. A necessary and sufficient condition for this integral flow to yield an R 1¦1-action is obtained: the homogeneous components, X0, and, X1, of the given field must define a Lie superalgebra of dimension (1, 1). The supergroup structure on R 1¦1, however, has to be specified: there are three non-isomorphic Lie supergroup structures on R 1¦1, all of which have addition as the group operation in the underlying …
Texture advection on discontinuous flows
2015
Texture advection techniques, which transport textures using a velocity field, are used to visualize the dynamics of a flow on a triangle mesh. Some flow phenomena lead to velocity fields with discontinuities that cause the deformation of the texture which is not properly controlled by these techniques. We propose a method to detect and visualize discontinuities on a flow, keeping consistent texture advection at both sides of the discontinuity. The method handles the possibility that the discontinuity travels across the domain of the flow with arbitrary velocity, estimating its speed with least-squares approximation. The technique is tested with different sample scenarios and with two avala…