Locally connected simplicial maps

In Propositions 1.6 and 7.6 of his paper onp-group complexes of finite groups [5], Quillen establishes fundamental results comparing the homology and the fundamental group of the order complexes of posetsP, Q admitting a mapf :P →Q of posets with good local behavior. We prove the analogue of Quillen’s results for mapsf :K→L of simplicial complexesK andL in a more general setup. This work was partially supported by BSF 88-00164. The first author is partially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032.     

Self-deflection and all-optical beam steering in CdZnTe

We report on the experimental observation of very large self-deflection of optical beams, along with all-optical steering, and electro-optic beam deflection. We observe as many as 27 resolvable spots of deflection at 1-W/cm2 intensity. These deflections arise from enhanced photorefractive effects in CdZnTe:V, giving rise to optically induced index changes in excess of 0.08, which is to our knowledge the strongest nonlinearity ever reported for any bulk semiconductor.     

Evanescent-wave mirror for ultracold diatomic polar molecules

We describe the interaction of an ultracold diatomic polar molecule with an evanescent-wave mirror. Several features of this system are explored, such as the coupling between internal rovibrational states of the molecule and the laser field. Numerical simulations show quantum reflection and state selection under attainable physical conditions. Such molecular optics components will facilitate the manipulation and trapping of ultracold molecules, and might serve in future applications in several fields, e.g., as devices to filter and select a state for ultracold chemistry, to measure extremely low temperatures of molecules, or to manipulate states for quantum information processing.     

Elliptic incoherent solitons in saturable nonlinear media

We identify elliptic incoherent spatial solitons in isotropic saturable nonlinear media. These solitary states are possible, provided that their correlation function is anisotropic. The propagation dynamics of this new class of solitons are investigated by use of numerical simulations. We find that, during a collision event of two such elliptic solitons, their intensity ellipse rotates, and at the same time their centers of gravity tend to revolve around each other.     

Long term behavior of lithographically prepared in vitro neuronal networks

We measured the long term spontaneous electrical activity of neuronal networks with different sizes, grown on lithographically prepared substrates and recorded with multi-electrode-array technology. The time sequences of synchronized bursting events were used to characterize network dynamics. All networks exhibit scale-invariant Lévy distributions and long-range correlations. These observations suggest that different-size networks self-organize to adjust their activities over many time scales. As predictions of current models differ from our observations, this calls for revised models.     

Valuation-like maps and the congruence subgroup property

Let D be a finite dimensional division algebra and N a subgroup of finite index in D ^×. A valuation-like map on N is a homomorphism ϕ:N?Γ from N to a (not necessarily abelian) linearly ordered group Γ satisfying N _<-α+1⊆N _<-α for some nonnegative α∈Γ such that N _<-α≠=?, where N _<-α={x∈N|ϕ(x)<-α}. We show that this implies the existence of a nontrivial valuation v of D with respect to which N is (v-adically) open. We then show that if N is normal in D ^× and the diameter of the commuting graph of D ^×/N is ≥4, then N admits a valuation-like map. This has various implication; in particular it restricts the structure of finite quotients of D ^×. The notion of a valuation-like map is inspired by [27], and in fact is closely related to part (U3) of the U-Hypothesis in [27]. Oblatum 14-VII-2000 & 22-XI-2000?Published online: 5 March 2001     

Self-accelerating self-trapped optical beams

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Self-accelerating self-trapped wave packets are universal, and can also be found in matter waves, plasma, etc.     

Simply connected coset complexes for rank 1 groups of Lie type

This work was partially supported by BSF 92-00320