Barkhausen Noise in a Relaxor Ferroelectric

Barkhausen noise, including both periodic and aperiodic components, is found in and near the relaxor regime of a familiar relaxor ferroelectric, PbMg$_{1/3}$Nb$_{2/3}$O$_3$, driven by a periodic electric field. The temperature dependences of both the amplitude and spectral form show that the size of the coherent dipole moment changes shrink as the relaxor regime is entered, contrary to expectations based on some simple models.Comment: 4 pages RevTeX4, 5 figures; submitted to Phys Rev Let

Using mixed data in the inverse scattering problem

Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the $r_{n}(E)$ range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum Scattering Theory, Hungary, August 200

A study on the effect of dislocation on the magnetic properties of nickel using magnetic NDE methods

Dislocations affect the magnetic properties of ferromagnetic materials by pinning the domain walls. The primary mechanism is interaction between the stress fields of dislocation and domain walls. Using magnetic nondestructive methods, namely the acoustic Barkhausen noise (AB), magnetic Barkhausen noise (MB), and the hysteresis curves, we have studied these interactions. The three measurements give different types of information. AB provides information about non‐180° type domain wall interaction, MB primarily provides information about 180° domain wall interaction, and the hysteresis curve about both these interactions as well as about rotation of domain walls. The paper presents results obtained on polycrystalline nickel which was first deformed and then annealed at different temperatures in order to achieve different dislocation densities. The results show that AB and hysteresis loss follow the same trend as hardness. MB results, however, change in a more complex fashion which is sensitive to grain recrystallization as well as dislocation structure. Interesting features of these results will be discussed in detail

Massey products in symplectic manifolds

The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are exposed. The construction uses the symplectic blow-up and is based on the author results, which describe conditions under which the blow-up of a symplectic manifold X along its submanifold Y inherits nontrivial Massey products from X ot Y. This gives a general construction of nonformal symplectic manifolds.Comment: LaTeX, 48 pages, 2 figure

Linking and causality in globally hyperbolic spacetimes

The linking number $lk$ is defined if link components are zero homologous. Our affine linking invariant $alk$ generalizes $lk$ to the case of linked submanifolds with arbitrary homology classes. We apply $alk$ to the study of causality in Lorentz manifolds. Let $M^m$ be a spacelike Cauchy surface in a globally hyperbolic spacetime $(X^{m+1}, g)$. The spherical cotangent bundle $ST^*M$ is identified with the space $N$ of all null geodesics in $(X,g).$ Hence the set of null geodesics passing through a point $x\in X$ gives an embedded $(m-1)$-sphere $S_x$ in $N=ST^*M$ called the sky of $x.$ Low observed that if the link $(S_x, S_y)$ is nontrivial, then $x,y\in X$ are causally related. This motivated the problem (communicated by Penrose) on the Arnold's 1998 problem list to apply link theory to the study of causality. The spheres $S_x$ are isotopic to fibers of $(ST^*M)^{2m-1}\to M^m.$ They are nonzero homologous and $lk(S_x,S_y)$ is undefined when $M$ is closed, while $alk(S_x, S_y)$ is well defined. Moreover, $alk(S_x, S_y)\in Z$ if $M$ is not an odd-dimensional rational homology sphere. We give a formula for the increment of \alk under passages through Arnold dangerous tangencies. If $(X,g)$ is such that $alk$ takes values in $\Z$ and $g$ is conformal to $g'$ having all the timelike sectional curvatures nonnegative, then $x, y\in X$ are causally related if and only if $alk(S_x,S_y)\neq 0$. We show that $x,y$ in nonrefocussing $(X, g)$ are causally unrelated iff $(S_x, S_y)$ can be deformed to a pair of $S^{m-1}$-fibers of $ST^*M\to M$ by an isotopy through skies. Low showed that if (\ss, g) is refocussing, then $M$ is compact. We show that the universal cover of $M$ is also compact.Comment: We added: Theorem 11.5 saying that a Cauchy surface in a refocussing space time has finite pi_1; changed Theorem 7.5 to be in terms of conformal classes of Lorentz metrics and did a few more changes. 45 pages, 3 figures. A part of the paper (several results of sections 4,5,6,9,10) is an extension and development of our work math.GT/0207219 in the context of Lorentzian geometry. The results of sections 7,8,11,12 and Appendix B are ne

Domain wall dynamics and Barkhausen effect in metallic ferromagnetic materials. II. Experiments

Barkhausen effect (BE) phenomenology in iron‐based ferromagnetic alloys is investigated by a proper experimental method, in which BE experiments are restricted to the central part of the hysteresis loop, and the amplitude probability distribution, P0(Φ), and power spectrum, F(ω), of the B flux rate Φ are measured under controlled values of the magnetization rate and differential permeability μ. It is found that all of the experimental data are approximately consistent with the law P0(Φ)∝Φ−1 exp(−Φ/〈Φ〉), where all dependencies on and μ are described by the single dimensionless parameter >0. Also the parameters describing the shape of F(ω) are found to obey remarkably simple and general laws of dependence on and μ. The experimental results are interpreted by means of the Langevin theory of domain‐wall dynamics proposed in a companion paper. The theory is in good agreement with experiments, and permits one to reduce the basic aspects of BE phenomenology to the behavior of two parameters describing the stochastic fluctuations of the local coercive field experienced by a moving domain wall

Dwyer-Kan homotopy theory of enriched categories

We construct a model structure on the category of small categories enriched over a combinatorial closed symmetric monoidal model category satisfying the monoid axiom. Weak equivalences are Dwyer-Kan equivalences, i.e. enriched functors which induce weak equivalences on morphism objects and equivalences of ordinary categories when we take sets of connected components on morphism objects.Comment: 39 pages, corrected versio