2,025 research outputs found
The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
We show that for two dimensional manifolds M with negative Euler
characteristic there exists subsets of the space of smooth Riemannian metrics
which are invariant and either parabolic or backwards-parabolic for the 2nd
order RG flow. We also show that solutions exists globally on these sets.
Finally, we establish the existence of an eternal solution that has both a UV
and IR limit, and passes through regions where the flow is parabolic and
backwards-parabolic
Rate of Convergence of Space Time Approximations for stochastic evolution equations
Stochastic evolution equations in Banach spaces with unbounded nonlinear
drift and diffusion operators driven by a finite dimensional Brownian motion
are considered. Under some regularity condition assumed for the solution, the
rate of convergence of various numerical approximations are estimated under
strong monotonicity and Lipschitz conditions. The abstract setting involves
general consistency conditions and is then applied to a class of quasilinear
stochastic PDEs of parabolic type.Comment: 33 page
Abelian groups as artinian or noetherian modules above endomorphism rings
The A and B Abellian groups, such that the Hom(A, B) homomorphism group is the Artin module over the ring of the B group endomorphism, are described. Description of the A and B group for which the Hom(A,B) group is the Artin module over the ring of the A group endomorphism is reduced to the case when the A group has no torsion and the B group is either a quasi-cyclic group or a divisible group without torsion. The A and B Abellian groups for which the Hom(A,B) group is the Neter module over the E(A) or E(B) ring are characterized. The research of arbitrary Abellian group with the link Neter ring of endomorphisms is reduced to the research of the group without torsion with the link Neter ring of endomorphisms. The research of the right Neter ring of endomorphisms remained uncompleted. The separable Abele groups without torsion with the link and right Neter rings of endomorphisms are described
Wave-like aquatic propulsion of mono-hull marine vessels
The present paper describes the results of the experimental investigation of a small-scale mono-hull model boat propelled by a localised flexural wave propagating along the plate of finite width forming the boat’s keel. Forward propulsion of the boat was achieved through flexural wave propagation in the opposite direction, which is similar to the aquatic propulsion used in nature by stingrays. The model boat under consideration underwent a series of tests both in a Perspex water tank and in the
experimental pool. In particular, the forward velocity of the boat has been measured for
different frequencies and amplitudes of the flexural wave. The highest velocity achieved
was 32 cm/s. The thrust and propulsive efficiency have been measured as well. The
obtained value of the propulsive efficiency in the optimum regime was 51%. This
indicates that efficiency of this type of aquatic propulsion is comparable to that of
dolphins and sharks (around 75%) and to that of a traditional propeller (around 70%). In
contrast to a propeller though, the wave-like aquatic propulsion has the following
advantages: it does not generate underwater noise and it is safe for people and marine
animals
Experimental investigation of a mono-hull model boat with wave-like aquatic propulsion
Experimental investigation of a mono-hull model boat with wave-like aquatic propulsio
Towards a feasible implementation of quantum neural networks using quantum dots
We propose an implementation of quantum neural networks using an array of
quantum dots with dipole-dipole interactions. We demonstrate that this
implementation is both feasible and versatile by studying it within the
framework of GaAs based quantum dot qubits coupled to a reservoir of acoustic
phonons. Using numerically exact Feynman integral calculations, we have found
that the quantum coherence in our neural networks survive for over a hundred ps
even at liquid nitrogen temperatures (77 K), which is three orders of magnitude
higher than current implementations which are based on SQUID-based systems
operating at temperatures in the mK range.Comment: revtex, 5 pages, 2 eps figure
Chaos edges of -logistic maps: Connection between the relaxation and sensitivity entropic indices
Chaos thresholds of the -logistic maps are numerically analysed at accumulation points of cycles 2, 3
and 5. We verify that the nonextensive -generalization of a Pesin-like
identity is preserved through averaging over the entire phase space. More
precisely, we computationally verify , where the entropy (), the sensitivity to the initial
conditions , and
(). The entropic index
depend on
both and the cycle. We also study the relaxation that occurs if we start
with an ensemble of initial conditions homogeneously occupying the entire phase
space. The associated Lebesgue measure asymptotically decreases as
(). These results led to (i) the first
illustration of the connection (conjectured by one of us) between sensitivity
and relaxation entropic indices, namely , where the positive numbers depend on the
cycle; (ii) an unexpected and new scaling, namely ( for , and for ).Comment: 5 pages, 5 figure
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