173 research outputs found
Many Higgs doublet supersymmetric model, flavor changing interactions and spontaneous CP violation
I study many higgs doublet supersymmetric model with spontaneous CP violation. The damaging flavor changing interactions and large CP violation are brought under control simultaneously by an approximate PQ symmetry. I relate the smallness of the CP violating parameter in the kaon system to the small {m_b \over m_t} ratio
Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
The application of the Gardner method for generation of conservation laws to
all the ABS equations is considered. It is shown that all the necessary
information for the application of the Gardner method, namely B\"acklund
transformations and initial conservation laws, follow from the multidimensional
consistency of ABS equations. We also apply the Gardner method to an asymmetric
equation which is not included in the ABS classification. An analog of the
Gardner method for generation of symmetries is developed and applied to
discrete KdV. It can also be applied to all the other ABS equations
Characteristics of Conservation Laws for Difference Equations
Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the converse of Noether's Theorem. Transferring these results to difference equations is nontrivial, largely because difference operators are not derivations and do not obey the chain rule for derivatives. We show how these problems may be resolved and illustrate various uses of the characteristic. In particular, we establish the converse of Noether's Theorem for difference equations, we show (without taking a continuum limit) that the conservation laws in the infinite family generated by Rasin and Schiff are distinct, and we obtain all five-point conservation laws for the potential Lotka-Volterra equation
Spontaneous CP violation in supersymmetric models with four Higgs doublets
We consider supersymmetric extensions of the standard model with two pairs of Higgs doublets. We study the possibility that CP violation is generated spontaneously in the scalar sector via vacuum expectation values (VEVs) of the Higgs fields. Using a simple geometrical interpretation of the minimum conditions we prove that the minimum of the tree-level scalar potential for these models is allways real. We show that complex VEVs can appear once radiative corrections and/or explicit {\it soft} CP violating terms are added to the effective potential
Extension of the Adler-Bobenko-Suris classification of integrable lattice equations
The classification of lattice equations that are integrable in the sense of
higher-dimensional consistency is extended by allowing directed edges. We find
two cases that are not transformable via the 'admissible transformations' to
the lattice equations in the existing classification.Comment: 14 pages, 2 figure
Effects of shear on eggs and larvae of striped bass, morone saxatilis, and white perch, M. americana
Shear stress, generated by water movement, can kill fish eggs and larvae by causing rotation or deformation. Through the use of an experimental apparatus, a series of shear
(as dynes/cm2)-mortality equations for fixed time exposures were generated for striped bass and white perch eggs and larvae. Exposure of striped bass eggs to a shear level of 350 dynes/cm2 kills 36% of the eggs in 1 min; 69% in 2 min, and 88% in 4 min; exposure of larvae to 350 dynes/cm2 kills 9.3% in 1 min, 30.0% in 2 min, and 68.1% in 4 min. A shear level of 350 dynes/cm2 kills 38% of the white perch eggs in 1 min, 41% in 2 min, 89% in 5 min, 96% in 10 min, and 98% in 20 min. A shear level of 350 dynes/cm2 applied to white perch larvae destroys 38% of the larvae in 1 min, 52% in 2 min, and 75% in 4 min. Results are experimentally used in conjunction with the determination of shear levels in the Chesapeake and Delaware Canal and ship movement for the estimation of fish egg and larval mortalities in the field
An algebraic method of classification of S-integrable discrete models
A method of classification of integrable equations on quad-graphs is
discussed based on algebraic ideas. We assign a Lie ring to the equation and
study the function describing the dimensions of linear spaces spanned by
multiple commutators of the ring generators. For the generic case this function
grows exponentially. Examples show that for integrable equations it grows
slower. We propose a classification scheme based on this observation.Comment: 11 pages, workshop "Nonlinear Physics. Theory and Experiment VI",
submitted to TM
Infinitely many conservation laws for the discrete KdV equation
In \cite{RH3} Rasin and Hydon suggested a way to construct an infinite number
of conservation laws for the discrete KdV equation (dKdV), by repeated
application of a certain symmetry to a known conservation law. It was not
decided, however, whether the resulting conservation laws were distinct and
nontrivial. In this paper we obtain the following results: (1) We give an
alternative method to construct an infinite number of conservation laws using a
discrete version of the Gardner transformation. (2) We give a direct proof that
the Rasin-Hydon conservation laws are indeed distinct and nontrivial. (3) We
consider a continuum limit in which the dKdV equation becomes a first-order
eikonal equation. In this limit the two sets of conservation laws become the
same, and are evidently distinct and nontrivial. This proves the nontriviality
of the conservation laws constructed by the Gardner method, and gives an
alternate proof of the nontriviality of the conservation laws constructed by
the Rasin-Hydon method
Construction of Integrals of Higher-Order Mappings
We find that certain higher-order mappings arise as reductions of the
integrable discrete A-type KP (AKP) and B-type KP (BKP) equations. We find
conservation laws for the AKP and BKP equations, then we use these conservation
laws to derive integrals of the associated reduced maps.Comment: appear to Journal of the Physical Society of Japa
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