1,132 research outputs found
New approach to interpretation of airborne magnetic and electromagnetic data
Journal ArticleWe present a new technique for underground imaging based on the idea of space-frequency filtering and downward continuation of the observed airborne magnetic and electromagnetic data. The technique includes two major methods. The first method is related to the downward analytical continuation and is based on the calculation of the total normalized gradient of the observed field. The second method is based on Wiener filtering and takes into account a priori information about typical AEM anomaly shape from a possible target
On the classification of conditionally integrable evolution systems in (1+1) dimensions
We generalize earlier results of Fokas and Liu and find all locally analytic
(1+1)-dimensional evolution equations of order that admit an -shock type
solution with .
To this end we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we
completely characterized all (1+1)-dimensional evolution systems
\bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n) that are
conditionally invariant under a given generalized (Lie--B\"acklund) vector
field \bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u} under
the assumption that the system of ODEs \bi{Q}=0 is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a
system of ODEs in , thus being a nonlinear counterpart to quasi-exactly
solvable models in quantum mechanics.
Keywords: Exact solutions, nonlinear evolution equations, conditional
integrability, generalized symmetries, reduction, generalized conditional
symmetries
MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34Comment: 8 pages, LaTeX 2e, now uses hyperre
Group classification of heat conductivity equations with a nonlinear source
We suggest a systematic procedure for classifying partial differential
equations invariant with respect to low dimensional Lie algebras. This
procedure is a proper synthesis of the infinitesimal Lie's method, technique of
equivalence transformations and theory of classification of abstract low
dimensional Lie algebras. As an application, we consider the problem of
classifying heat conductivity equations in one variable with nonlinear
convection and source terms. We have derived a complete classification of
nonlinear equations of this type admitting nontrivial symmetry. It is shown
that there are three, seven, twenty eight and twelve inequivalent classes of
partial differential equations of the considered type that are invariant under
the one-, two-, three- and four-dimensional Lie algebras, correspondingly.
Furthermore, we prove that any partial differential equation belonging to the
class under study and admitting symmetry group of the dimension higher than
four is locally equivalent to a linear equation. This classification is
compared to existing group classifications of nonlinear heat conductivity
equations and one of the conclusions is that all of them can be obtained within
the framework of our approach. Furthermore, a number of new invariant equations
are constructed which have rich symmetry properties and, therefore, may be used
for mathematical modeling of, say, nonlinear heat transfer processes.Comment: LaTeX, 51 page
Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras
We give a complete point-symmetry classification of all third-order evolution
equations of the form
which admit semi-simple symmetry algebras and extensions of these semi-simple
Lie algebras by solvable Lie algebras. The methods we employ are extensions and
refinements of previous techniques which have been used in such
classifications.Comment: 53 page
Catalytic CO Oxidation on Nanoscale Pt Facets: Effect of Inter-Facet CO Diffusion on Bifurcation and Fluctuation Behavior
We present lattice-gas modeling of the steady-state behavior in CO oxidation
on the facets of nanoscale metal clusters, with coupling via inter-facet CO
diffusion. The model incorporates the key aspects of reaction process, such as
rapid CO mobility within each facet, and strong nearest-neighbor repulsion
between adsorbed O. The former justifies our use a "hybrid" simulation approach
treating the CO coverage as a mean-field parameter. For an isolated facet,
there is one bistable region where the system can exist in either a reactive
state (with high oxygen coverage) or a (nearly CO-poisoned) inactive state.
Diffusion between two facets is shown to induce complex multistability in the
steady states of the system. The bifurcation diagram exhibits two regions with
bistabilities due to the difference between adsorption properties of the
facets. We explore the role of enhanced fluctuations in the proximity of a cusp
bifurcation point associated with one facet in producing transitions between
stable states on that facet, as well as their influence on fluctuations on the
other facet. The results are expected to shed more light on the reaction
kinetics for supported catalysts.Comment: 22 pages, RevTeX, to appear in Phys. Rev. E, 6 figures (eps format)
are available at http://www.physik.tu-muenchen.de/~natali
Underground imaging by frequency-domain electromagnetic migration
Journal ArticleA new method of the resistivity imaging based on frequency-domain electromagnetic migration is developed. Electromagnetic (EM) migration involves downward diffusion of observed EM fields whose time flow has been reversed. Unlike downward analytical continuation, migration is a stable procedure that accurately restores the phase of the upgoing field inside the Earth. This method is indented for the processing and interpretation of EM data collected for both TE and TM modes of plane-wave excitation. Until recently, the method could be applied only for determining the position of anomalous structures and for finding interfaces between layers of different conductivity. There were no well developed approaches to the resistivity imaging, which is the key problem in the inversion of EM data. We provide a novel approach to determining not only the position of anomalous structures but their resistivity as well. The main difficulty in the practical realization of this approach is determining the background resistivity distribution for migration. We discuss the method of the solution of this problem based on differential transformation of apparent resistivity curves. The final goal of migration is to provide a first order interpretation using a computational effort equivalent to a forward modeling calculation
Melaspilea galligena sp. nov. and some other lichenicolous fungi from Russia
Thirty species of lichenicolous fungi are reported, many being new to various regions of Russia. Melaspilea galligena sp. nov. growing on Pertusaria cf. cribellata is described from Russian Far East. A possibly new lichenicolous Toninia species (on Parmelina tiliacea) and a species of Arthonia (on Cladonia) with 1–2-septate ascospores resembling poorly known A. lepidophila are described, illustrated and discussed. Dactylospora suburceolata is reported new to Russia and Asia, growing on a new host species Mycobilimbia carneoalbida. Tremella cetrariicola is new to Siberia and Clypeococcum cetrariae is newly documented on Vulpicida.
Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general
investigations on transformational properties of classes of differential
equations is proposed. It is based on mappings between classes of differential
equations, generated by families of point transformations. A class of variable
coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the
general form () is studied from the
symmetry point of view in the framework of the approach proposed. The singular
subclass of the equations with is singled out. The group classifications
of the entire class, the singular subclass and their images are performed with
respect to both the corresponding (generalized extended) equivalence groups and
all point transformations. The set of admissible transformations of the imaged
class is exhaustively described in the general case . The procedure of
classification of nonclassical symmetries, which involves mappings between
classes of differential equations, is discussed. Wide families of new exact
solutions are also constructed for equations from the classes under
consideration by the classical method of Lie reductions and by generation of
new solutions from known ones for other equations with point transformations of
different kinds (such as additional equivalence transformations and mappings
between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica
New variable separation approach: application to nonlinear diffusion equations
The concept of the derivative-dependent functional separable solution, as a
generalization to the functional separable solution, is proposed. As an
application, it is used to discuss the generalized nonlinear diffusion
equations based on the generalized conditional symmetry approach. As a
consequence, a complete list of canonical forms for such equations which admit
the derivative-dependent functional separable solutions is obtained and some
exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig
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