Realization of reflectionless potentials in photonic lattices

We realize experimentally a true reflectionless potential, which facilitates nonresonant unity transmission for all incident waves and at the same time supports localized modes. We utilize arrays of evanescently coupled optical waveguides, where a particular modulation of the transverse waveguide separations provides a physical realization of reflectionless Ablowitz-Ladik soliton potentials.     

Transannular additions of selectfluor and xenon difluoride: regioselectivity and mechanism

The addition of 1‐chloromethyl‐4‐fluoro‐1,4‐diazoniabicyclo[2.2.2]octane bis‐tetrafluoroborate (F‐TEDA) to unsaturated systems was modelled computationally at the ab initio levels and studied experimentally. The reaction of olefins with F‐TEDA is driven exclusively by charge transfer and displays the antibonding orbital picture in the transition structure for F‐transfer, similarly to that for the reactions of olefins with F‐radical. In contrast, the electrophilic and concerted fluorinations, respectively with H₂O???F⁺ complex and with F₂, show strong bonding interactions between the fluorine and olefin moieties in the transition structures. The reaction with F‐TEDA involves an initial formation of highly delocalized charge‐transfer complexes in the first step with further low‐barrier (ca 4 kcal) migration of fluorine and is best described as an inner‐sphere electron transfer. This nonelectrophilic mechanism is operative for the transannular addition of F‐TEDA to 3‐methylene‐7‐ethylidenebicyclo[3.3.1]nonane studied experimentally. The addition mode is determined by the formation of a more stable complex via the ethylidene fragment and demonstrates selectivities that differ from conventional electrophilic additions. This mechanistic scenario may be extended to the fluorination with xenon difluoride where similar products are formed in high yields. Copyright © 2010 John Wiley & Sons, Ltd.     

A four kinetic state model of fast axonal transport: Model formulation and perturbation solution

This paper formulates a four kinetic state model for fast axonal transport. The paper further develops the Smith-Simmons model that is based on equations governing intracellular molecular-motor-assisted transport; these equations are extended by considering four rather than three kinetic states for organelles. The model considers plus-end and minus-end-oriented organelles that can be either free (suspended in the cytosol) or attached to microtubules (MTs) (in the latter case organelles are transported by molecular motors). The paper then develops a method for uncoupling differential equations of the proposed model. A perturbation solution of this problem is obtained. The effect of transition between plus-end-oriented and minus-end oriented organelles is discussed. The accuracy of the obtained perturbation solution is evaluated by comparing the zero-order and the first-order results with a high-accuracy numerical solution.     

Analytical investigation of various regimes of retrograde trafficking of neurotropic viruses in axons

A model of retrograde axonal transport of neurotropic viruses is developed. The model accounts for active viral transport by dynein motors as well as for passive transport by diffusion; the destruction of the virus as it propagates toward the neuron soma is modeled utilizing a first-order decay rate process. The effect of a limited time during which the axonal synapse is exposed to the virus is incorporated. An analytical solution is obtained. The obtained solution makes it possible to identify four different regimes of viral transport in the axon that correspond to the following situations: (1) Small viral diffusivity and small rate of viral destruction; (2) Large viral diffusivity and small rate of viral destruction; (3) Small viral diffusivity and large rate of viral destruction; (4) Large viral diffusivity and large rate of viral destruction. Characteristic features of these regimes are discussed.     

Degenerate band edges in optical fiber with multiple grating: efficient coupling to slow light

Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings. The enhanced coupling near a DBE occurs because of the presence of one or more evanescent modes, which are absent at conventional quadratic band edges. We furthermore show that the coupling can be increased or suppressed by varying the number of excited evanescent waves.     

Effect of coherence and polarization on resolution of optical imaging system

The effect of coherence properties of illumination on image resolution, well known in a scalar case, is studied for the case of vector electromagnetic illumination. Using an example of vector Gaussian Schell-model illumination, we analyze the dependence of optical system resolution on the transverse correlation lengths of the orthogonal field components and on the ratio of the powers of these components, each taken separately.     

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.     

On the nuclear modification factor at RHIC and LHC

We show that pQCD factorization incorporated with pre-hadronization energy-loss effect naturally leads to flatness of the nuclear modification factor RAA$R_{\mathit{AA}}$ for produced hadrons at high transverse momentum pT$p_T$. We consider two possible scenarios for the pre-hadronization: In scenario 1, the produced gluon propagates through dense QCD medium and loses energy. In scenario 2, all gluons first decay to quark–antiquark pairs and then each pair loses energy as propagating through the medium. We show that the estimates of the energy-loss in these two different models lead to very close values and is able to explain the suppression of high-pT$p_T$ hadrons in nucleus–nucleus collisions at RHIC. We show that the onset of the flatness of RAA$R_{\mathit{AA}}$ for the produced hadron in central collisions at midrapidity is about pT≈15$p_T\approx 15$ and 25 GeV at RHIC and the LHC energies, respectively. We show that the smallness (RAA<0.5$R_{\mathit{AA}}<0.5$ ) and the high-pT$p_T$ flatness of RAA$R_{\mathit{AA}}$ obtained from the kT$k_T$ factorization supplemented with the Balitsky–Kovchegov (BK) equation is rather generic and it does not strongly depend on the details of the BK solutions. We show that energy-loss effect reduces the nuclear modification factor obtained from the kT$k_T$ factorization about 30–50% at moderate pT$p_T$.     

New observables in topological instantonic field theories

Instantonic theories are quantum field theories where all correlators are determined by integrals over the finite-dimensional space (space of generalized instantons). We consider novel geometrical observables in instantonic topological quantum mechanics that are strikingly different from standard evaluation observables. These observables allow jumps of special type for the trajectory (at the point of insertion of such observables). They do not (anti)commute with evaluation observables and raise the dimension of the space of allowed configurations, while the evaluation observables lower this dimension. We study these observables in geometric and operator formalisms. Simple examples are explicitly computed; they depend on the linking of points.     

Theoretical analysis of an optimal control problem of conductive–convective–radiative heat transfer

The problem of optimal heat removal from a three-dimensional domain is considered. The specific of the study consist in accounting for the radiative heat transfer. The so-called P₁ approximation of the radiative heat transfer equation is used, which reduces the model to a nonlinear elliptic system. A problem of optimal boundary control of this system is considered. The solvability of the control problem is proved, and necessary optimality conditions of first order are derived. Examples of non-singularity of these conditions are given.