Effective field theory for the SO(n) bilinear-biquadratic spin chain

We present a low-energy effective field theory to describe the SO(n) bilinear-biquadratic spin chain. We start with n=6 and construct the effective theory by using six Majorana fermions. After determining various correlation functions, we characterize the phases and establish the relation between the effective theories for SO(6) and SO(5). Together with the known results for n=3 and 4, a reduction mechanism is proposed to understand the ground state for arbitrary SO(n). Also, we provide a generalization of the Lieb-Schultz-Mattis theorem for SO(n). The implications of our results for entanglement and correlation functions are discussed.     

Chromogenic and fluorogenic sensing of Cu based on coumarin

A new highly selective, reversible, chromogenic, and fluorogenic chemosensor (4) based on thiazole-coumarin moieties for quantification of copper ions in aqueous-DMSO was designed and synthesized. The mechanism of fluorescence was based on ICT, which was modified by the introduction of an electron-donating diethylamino group making it chromogenic and increasing the binding affinity. The selectivity toward copper ions was not affected by the presence of representative alkali metals, alkali earth metals, or other transition metals.     

Acylindrical accessibility for groups

We define the notion of acylindrical graph of groups of a group. We bound the combinatorics of these graphs of groups for f.g. freely indecomposable groups. Our arguments imply the finiteness of acylindrical surfaces in closed 3-manifolds [Ha], finiteness of isomorphism classes of small splittings of (torsion-free) freely indecomposable hyperbolic groups as well as finiteness results for small splittings of f.g. Kleinian and semisimple discrete groups acting on non-positively curved simply connected manifolds. In order to get our accessibility for f.g. groups we generalize parts of Rips' analysis of stable actions of f.p. groups on real trees to f.g. groups. The concepts we present play an essential role in constructing the canonical JSJ decomposition ([Se1],[Ri-Se2]), in obtaining the Hopf property for hyperbolic groups [Se2], and in our study of sets of solutions to equations in a free group [Se3]. Oblatum 30-IV-1992 & 1-X 1996     

Pyrolysis of diethyl carbonate: Shock-tube and flow-reactor measurements and modeling

Shock-tube and flow-reactor experiments were used to study the thermal decomposition of diethyl carbonate (C₂H₅OC(O)OC₂H₅; DEC). The formation of CO₂, C₂H₄, and C₂H₅OH was measured with gas chromatography/mass spectrometry (GC/MS) and high-repetition-rate time-of-flight mass spectrometry (HRR-TOF-MS) behind reflected shock waves. The same products were also detected by GC/MS in flow reactor experiments. All experiments combined span a temperature range of 663–1203 K at pressures between 1.0 and 2.0 bar. Time-resolved species concentration profiles from HRR-TOF-MS and product compositions from GC/MS measurements were simulated applying a detailed reaction mechanism for DEC combustion. A master-equation analysis was conducted based on computed energies from G4 calculations. Quantum chemical calculations confirm that DEC primarily decomposes by six-center elimination, C₂H₅OC(O)OC₂H₅ → C₂H₄ + C₂H₅OC(O)OH (1a), followed by rapid decomposition of the alkoxy acid, C₂H₅OC(O)OH → C₂H₅OH + CO₂ (1b). Measured DEC decomposition rate constants k(T) at p ≈ 1.5 bar can be represented by the Arrhenius equation k(T) = 10^13.64±0.12 exp(?204.24±1.95 kJ/mol/RT) s ^{? 1}. Theoretical predictions for k_1a were in good agreement with experimentally derived values. The theoretical analysis also included dipropyl carbonate (C₃H₇OC(O)OC₃H₇; DPC) decomposition and the reactivities of DEC and DPC are compared and discussed in the context of reactivity of dialkyl carbonates under pyrolytic conditions.     

Pretty good quantum state transfer in asymmetric graphs via potential

We construct infinite families of graphs in which pretty good state transfer can be induced by adding a potential to the nodes of the graph (i.e. adding a number to a diagonal entry of the adjacency matrix). Indeed, we show that given any graph with a pair of cospectral nodes, a simple modification of the graph, along with a suitable potential, yields pretty good state transfer between the nodes. This generalizes previous work, concerning graphs with an involution, to asymmetric graphs.     

Statistical Physics of Fracture Surfaces Morphology

Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich phenomenology of anomalous scaling. We argue that traditional models of fracture fail to reproduce this rich phenomenology and new ideas and concepts are called for. We present some recent models that introduce the effects of deviations from homogeneous linear elasticity theory on the morphology of fracture surfaces, successfully reproducing the multiscaling phenomenology at least in 1+1 dimensions. For surfaces in 2+1 dimensions we introduce novel methods of analysis based on projecting the data on the irreducible representations of the SO(2) symmetry group. It appears that this approach organizes effectively the rich scaling properties. We end up proposing new experiments in which the rotational symmetry is not broken, such that the scaling properties should be particularly simple.     

Diophantine geometry over groups VI: the elementary theory of a free group

This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the sixth paper we use the quantifier elimination procedure presented in the two parts of the fifth paper in the sequence, to answer some of A. Tarski’s problems on the elementary theory of a free group, and to classify finitely generated (f.g.) groups that are elementarily equivalent to a non-abelian f.g. free group. Received (resubmission): January 2004 Revision: January 2006 Accepted: January 2006 Partially supported by an Israel Academy of Sciences fellowship.     

Diophantine geometry over groups V2: quantifier elimination II

This paper is the sixth in a sequence on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the two papers on quantifier elimination we use the iterative procedure that validates the correctness of an AE sentence defined over a free group, presented in the fourth paper, to show that the Boolean algebra of AE sets defined over a free group is invariant under projections, hence, show that every elementary set defined over a free group is in the Boolean algebra of AE sets. The procedures we use for quantifier elimination, presented in this paper, enable us to answer affirmatively some of Tarski’s questions on the elementary theory of a free group in the last paper of this sequence. Received (resubmission): January 2004 Revision: November 2005 Accepted: March 2006 Partially supported by an Israel Academy of Sciences Fellowship.