Organizational Modes of Large-Scale Vortices in an Axisymmetric Turbulent Jet

Large vortices occurring in the axial plane of a self-similar axisymmetric turbulent jet are educed by spatially filtering PIV data. First, the instantaneous PIV frame is convolved with a Gaussian kernel to obtain a smooth (low-pass) field. Next, the low-pass field is Galilean transformed to expose the large vortices residing near the edges of the jet. Large vortices tend to organize themselves in preferred modes; evidence of ring and helical modes is revealed by Galilean transformation of the low-pass filtered field. Both modes seem to occur prominently in jets, with the helical mode being the more frequent. The overall diameter of both ring and helical modes is comparable with the local jet width. The low-pass field occasionally exhibits arrowhead shaped structures with large entrainment at their downstream tips. Stochastic estimates computed from the Galilean-transformed low-pass filtered field indicate that jet meander and a sweep-in of ambient fluid are sufficient to reconstruct large vortices. The frequency of occurrence of modes agrees with previously quoted results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rate independent hysteresis in a bi-stable chain

The nontrivial behavior of an elastic chain with identical bi-stable elements may be considered prototypical for a large number of nonlinear processes in solids ranging from phase transitions to fracture. The energy landscape of such a chain is extremely wiggly which gives rise to multiple equilibrium configurations and results in a hysteretic evolution and a possibility of trapping. In the present paper, which extends our previous study of the static equilibria in this system (Puglisi and Truskinovsky, J. Mech. Phys. Solids (2000) 1), we analyze the behavior of a bi-stable chain in a soft device under quasi-static loading. We assume that the system is over-damped and explore the variety of available nonequilibrium transformation paths. In particular, we show that the “minimal barrier” strategy leads to the localization of the transformation in a single spring. Loaded periodically, our bi-stable chain exhibits finite hysteresis which depends on the height of the admissible barrier; the cold work/heat ratio in this model is a fixed constant, proportional to the Maxwell stress. Comparison of the computed inner and outer hysteresis loops with recent experiments on shape memory wires demonstrates good qualitative agreement. Finally we discuss a relation between the present model and the Preisach model which is a formal interpolation scheme for hysteresis, also founded on the idea of bi-stability.     

Polymorphic phase transformations of 3‐chloro‐trans‐cinnamic acid and its solid solution with 3‐bromo‐trans‐cinnamic acid

We have investigated the polymorphic phase transformations above ambient temperature for 3‐chloro‐trans‐cinnamic acid (3‐ClCA, C₉H₇ClO₂) and a solid solution of 3‐ClCA and 3‐bromo‐trans‐cinnamic acid (3‐BrCA, C₉H₇BrO₂). At 413 K, the γ polymorph of 3‐ClCA transforms to the β polymorph. Interestingly, the structure of the β polymorph of 3‐ClCA obtained in this transformation is different from the structure of the β polymorph of 3‐BrCA obtained in the corresponding polymorphic transformation from the γ polymorph of 3‐BrCA, even though the γ polymorphs of 3‐ClCA and 3‐BrCA are isostructural. We also report a high‐temperature phase transformation from a γ‐type structure to a β‐type structure for a solid solution of 3‐ClCA and 3‐BrCA (with a molar ratio close to 1:1). The γ polymorph of the solid solution is isostructural with the γ polymorphs of pure 3‐ClCA and pure 3‐BrCA, while the β‐type structure produced in the phase transformation is structurally similar to the β polymorph of pure 3‐BrCA.     

Formation of Acetylene in the Reaction of Methane with Iron Carbide Cluster Anions FeC3− under High‐Temperature Conditions

The underlying mechanism for non‐oxidative methane aromatization remains controversial owing to the lack of experimental evidence for the formation of the first C?C bond. For the first time, the elementary reaction of methane with atomic clusters (FeC₃^?) under high‐temperature conditions to produce C?C coupling products has been characterized by mass spectrometry. With the elevation of temperature from 300 K to 610 K, the production of acetylene, the important intermediate proposed in a monofunctional mechanism of methane aromatization, was significantly enhanced, which can be well‐rationalized by quantum chemistry calculations. This study narrows the gap between gas‐phase and condensed‐phase studies on methane conversion and suggests that the monofunctional mechanism probably operates in non‐oxidative methane aromatization.     

Poisson Structures for Dispersionless Integrable Systems and Associated W-Algebras

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators . The reduction of the Poisson structure to the symplectic submanifold gives rise to W-algebras. In this Letter, we discuss properties of this Poisson structure, its Miura transformation and reductions. We are particularly interested in the following two cases: (a) L is pure polynomial in p with multiple roots and (b) L has multiple poles at finite distance. The w-algebra corresponding to the case (a) is defined as , where means the multiplicity of roots and to the case (b) is defined by where is the multiplicity of poles. We prove that -algebra is isomorphic via a transformation to U(1) with m= . We also give the explicit free fields representations for these W-algebras.     

A remark on Andrews-Askey integral

In this paper, we use the Andrews-Askey integral and the q-Chu-Vandermonde formula to derive a more general integral formula. Applications of the new integral formula are also given, which include to derive the q-Pfaff-Saalschütz formula and the terminating Sears's transformation formula.     

Nonexistence of Ground States of -△u = u^p - u^q

The authors use the method of moving spheres to prove the nonexistence of ground states of -△u = u^p - u^q for n≥3,-∞〈p〈（n＋2）/（n-2） and q〉max （1,p）,
In fact this conclusion is a special case of -△u =f（u） for n≥2.     

The Invariant and Quasi-invariant Transformations of the Stable Lévy Processes

Let ξ(t),t∈[0,1] be a strictly stable Lévy process with the index of stability α∈(0,2). By ℘ _ξ we denote the law of ξ in the Skorokhod space . For arbitrary ξ we construct ℘ _ξ -quasi-invariant semigroup of transformations of . Under some nondegeneracy condition on the spectral measure of the stable process we construct ℘ _ξ -quasi-invariant group of transformations of . In symmetric case this group is a group of the invariant transformations.