Radiationless Travelling Waves In Saturable Nonlinear Schr\"odinger Lattices

The longstanding problem of moving discrete solitary waves in nonlinear Schr{\"o}dinger lattices is revisited. The context is photorefractive crystal lattices with saturable nonlinearity whose grand-canonical energy barrier vanishes for isolated coupling strength values. {\em Genuinely localised travelling waves} are computed as a function of the system parameters {\it for the first time}. The relevant solutions exist only for finite velocities.Comment: 5 pages, 4 figure

Field scale limited irrigation scenarios for water policy strategies

ABSTRACT. Approaches to reducing irrigation inputs to crops have been studied for the past 50 to 60 years in research settings. Fewer efforts have been made to document limited irrigation responses over a number of seasons on commercial fields. This study compared farm−based irrigation management (FARM) with best management practices (BMP), late initiation of irrigation (LATE), and a restricted allocation (ALLOC). These irrigation management strategies each occupied 1/8 of a center pivot system in southwest Nebraska in continuous corn production, on four cooperating farms, which were replicated at the same sites for 3 to 6 years. Irrigation variables were achieved by irrigating or not irrigating, or by speeding up or slowing down the center pivot. When the grain yields and irrigation amounts were normalized each year using the FARM treatment as the basis, on average for three of four locations, the BMP treatment yielded equal to the FARM treatment, the LATE treatment yielded 93 % of the FARM treatment and the ALLOC yielded 84 % of the FARM treatment. At the same time, it took 76 % and 57 % of the water for the LATE and ALLOC treatments, respectively, to achieve these yields. The adjusted gross returns (yield price – irrigation treatment costs) of the irrigation treatments were analyzed for each location. When the gross returns were normalized using the FARM treatment as the basis, FARM and BMP returns were equal across combinations of high and low input commodity prices and pumping costs. The LATE treatment gross return was 95 % of FARM return. The gross return for the ALLOC treatment was 85 % to 91 % of the FARM treatment. The higher the water costs, the lower the difference between the highest and lowest returning water treatments. Relationships between evapotranspiratio

When is |C(X x Y)| = |C(X)||C(Y)|?

Sufficient conditions on the Tychonoff spaces X and Y are found that imply that the equation in the title holds. Sufficient conditions on the Tychonoff space X are found that ensure that the equation holds for every Tychonoff space Y . A series of examples (some using rather sophisticated cardinal arithmetic) are given that witness that these results cannot be generalized much

Radial Velocity Studies of Close Binary Stars. IX

Radial-velocity measurements and sine-curve fits to the orbital velocity variations are presented for the eighth set of ten close binary systems: AB And, V402 Aur, V445 Cep, V2082 Cyg, BX Dra, V918 Her, V502 Oph, V1363 Ori, KP Peg, V335 Peg. Half of the systems (V445 Cep, V2082 Cyg, V918 Her, V1363 Ori, V335 Peg) were discovered photometrically by the Hipparcos mission and all systems are double-lined (SB2) contact binaries. The broadening function method permitted improvement of the orbital elements for AB And and V502 Oph. The other systems have been observed for radial velocity variations for the first time; in this group are five bright (V<7.5) binaries: V445 Cep, V2082 Cyg, V918 Her, KP Peg and V335 Peg. Several of the studied systems are prime candidates for combined light and radial-velocity synthesis solutions.Comment: 17+ pages, 2 tables, 4 figure

Generating branes via sigma-models

Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations and assuming a block-diagonal form of a metric we derive a $(D-d)$-dimensional $\sigma$-model with the target space $SL(d,R)/SO(d) \times SL(2,R)/SO(2) \times R$ or its non-compact form. Various solution-generating techniques are developed and applied to construct some known and some new $p$-brane solutions. It is shown that the Harrison transformation belonging to the $SL(2,R)$ subgroup generates black $p$-branes from the seed Schwarzschild solution. A fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed as well as a non-linear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a non-trivial shell structure in the transverse space (`matrioshka' $p$-branes). It is shown that the $p$-brane intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. Finally, a Bonnor-type symmetry is used to construct a new magnetic 6-brane with a dipole moment in the ten-dimensional IIA theory.Comment: 21 pages Late

The Omega Deformation From String and M-Theory

We present a string theory construction of Omega-deformed four-dimensional gauge theories with generic values of \epsilon_1 and \epsilon_2. Our solution gives an explicit description of the geometry in the core of Nekrasov and Witten's realization of the instanton partition function, far from the asymptotic region of their background. This construction lifts naturally to M-theory and corresponds to an M5-brane wrapped on a Riemann surface with a selfdual flux. Via a 9-11 flip, we finally reinterpret the Omega deformation in terms of non-commutative geometry. Our solution generates all modified couplings of the \Omega-deformed gauge theory, and also yields a geometric origin for the quantum spectral curve of the associated quantum integrable system.Comment: LaTeX, 35 pages, 1 figure. Appendix on couplings of hypermultiplets in N=4 SYM adde

Modifications of the BTZ black hole by a dilaton/scalar

We investigate some modifications of the static BTZ black hole solution due to a chosen asymptotically constant dilaton/scalar. New classes of static black hole solutions are obtained. One of the solutions contains the Martinez-Zanelli conformal black hole solution as a special case. Using quasilocal formalism, we calculate their mass for a finite spatial region that contains the black hole. Their temperatures are also computed. Finally, using some of the curvature singularities as examples, we investigate whether a quantum particle behaves singularly or not.Comment: 18 pages, Latex, in press in Phys. Rev.

Nonlocal Field Theories and their Gravity Duals

The gravity duals of nonlocal field theories in the large N limit exhibit a novel behavior near the boundary. To explore this, we present and study the duals of dipole theories - a particular class of nonlocal theories with fundamental dipole fields. The nonlocal interactions are manifest in the metric of the gravity dual and type-0 string theories make a surprising appearance. We compare the situation to that in noncommutative SYM.Comment: 34pp LaTeX, minor corrections, reference adde

Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo