Counterintuitive versus regular inversionless gain in a coherently prepared ladder scheme

In this research we study lasing without population inversion from a three-level atom interacting with two laser fields, in the ladder or cascade scheme. We investigate counterintuitive sequencing as well as regular sequencing of the time of laser fields application. In a counterintuitive sequence scheme a short probe pulse is introduced prior to the application of the coupling field, in contrast, to a standard sequence scheme, where both fields are introduced at the same time. The influence of varying the probe pulse width and time delay between the initiation of probe and coupling fields on transient probe gain is investigated. The calculations indicate the potential of producing gain without inversion via counterintuitive sequence scheme.     

Two mechanisms of spiral-pair-source creation in excitable media

Two new modes of generating spiral pairs in an excitable medium have been found. They depend on a geometrical structure (GS) inside the medium. This may be formed e.g. as a result of scars or fibrosis in the heart tissue, or artificially built in a chemical reaction substrate. Both sources involve a GS composed of a circular “convergent lens” bounded by two opaque “walls”. One mode can be induced by a single wave and behaves as a “flip-flop” type of a limit cycle. The other mode is generated by a train of plane waves impinging on the GS, and is created at the focus of the converging wave-fragments.     

High b-value q-space diffusion MRI in myelin-deficient rat spinal cords

In this study, we explore the effect of the lack of myelin on the diffusion characteristics and diffusion anisotropy obtained from high b-value q-space diffusion-weighted MRI (q-space DWI) in excised rat spinal cords. Twenty-one-day-old myelin-deficient (md) mutant (N=6) and control rats (N=6) were used in this study. The MRI protocol included multi-slice T(1), T(2), proton density (PD) MR images and high b-value q-space diffusion MRI measured perpendicular and parallel to the fibers of the spine. q-Space displacement and probability maps, in both directions, as well as displacement anisotropy maps, were computed from the diffusion data. At the end of the MRI protocol, representative spinal cords from both groups were subjected to electron microscopy (EM). The md spinal cords show different gray/white matter contrast in the T(1), T(2) and PD MR images as compared with controls. In addition, the mean displacement extracted from the high b-value q-space diffusion data was found to be dramatically higher in the white matter (WM) of the md spinal cords than the controls when diffusion was measured perpendicular and parallel to the fibers of the spine. However, interestingly, at the diffusion time used in the present study, the difference in the WM displacement anisotropies of the two groups was not found to be statistically significant. Myelin was found to have a pronounced effect on the diffusion characteristics of water in WM but less so on the diffusion anisotropy observed at the diffusion time used in the present study.     

On Bifurcations of Equilibria of Intrinsically Curved, Electrically Charged, Rod-like Structures that Model DNA Molecules in Solution

DNA molecules in the familiar Watson–Crick double helical B form can be treated as though they have rod-like structures obtained by stacking dominoes one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. These “dominoes” are called base pairs. A recently developed theory of sequence-dependent DNA elasticity (Coleman, Olson, & Swigon, J. Chem. Phys. 118:7127–7140, 2003) takes into account the observation that the step from one base pair to the next can be one of several distinct types, each having its own mechanical properties that depend on the nucleotide composition of the step. In the present paper, which is based on that theory, emphasis is placed on the fact that, as each base in a base pair is attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson–Crick structure, and each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair, which implies that each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to long range electrostatic forces that, because they are only partially screened out by positively charged counter ions, can render the molecule’s equilibrium configurations sensitive to changes in the concentration c of salt in the medium. When these electrostatic forces are taken into account, the equations of mechanical equilibrium for a DNA molecule with N + 1 base pairs are a system of μN non-linear equations, where μ, the number of kinematical variables describing the relative displacement and orientation of adjacent pairs is in general 6; it reduces to 3 when base-pair steps are assumed to be inextensible and non-shearable. As a consequence of the long-range electrostatic interactions of base pairs, the μN × μN Jacobian matrix of the equations of equilibrium is full. An efficient numerically stable computational scheme is here presented for solving those equations and determining the mechanical stability of the calculated equilibrium configurations. That scheme is employed to compute and analyze bifurcation diagrams in which c is the bifurcation parameter and to show that, for an intrinsically curved molecule, small changes in c can have a strong effect on stable equilibrium configurations. Cases are presented in which several stable configurations occur at a single value of c.      

Singular surfaces in a linear pursuit-evasion game with elliptical vectograms

In a linear pursuit-evasion game with elliptical vectograms, singular surfaces appear in the plane of symmetry containing the ellipses minor axes and, as a consequence, locally nonsmooth isocost tubes are generated. Both dispersal and attractive focal surfaces are encountered. The dispersal surface is a zone of initial conditions for trajectories leaving the plane of symmetry. Optimal trajectories attracted by the focal surface merge tangentially to the plane of symmetry and remain there until the boundary of the dispersal zone is reached. Determination of the saddle-point strategies in the focal surface leads to constructing the isocost surfaces in the entire game space.     

A Geometrical Approach to the Study¶of Unbounded Solutions¶of Quasilinear Parabolic Equations

In this article, we are interested in the existence and uniqueness of solutions for quasilinear parabolic equations set in the whole space ? ^N . We consider, in particular, cases when there is no restriction on the growth or the behavior of these solutions at infinity. Our model equation is the mean-curvature equation for graphs for which Ecker and Huisken have shown the existence of smooth solutions for any locally Lipschitz continuous initial data. We use a geometrical approach which consists in seeing the evolution of the graph of a solution as a geometric motion which is then studied by the so-called “level-set approach”. After determining the right class of quasilinear parabolic PDEs which can be taken into account by this approach, we show how the uniqueness for the original PDE is related to “fattening phenomena” in the level-set approach. Existence of solutions is proved using a local L ^∞ bound obtained by using in an essential way the level-set approach. Finally we apply these results to convex initial data and prove existence and comparison results in full generality, i.e., without restriction on their growth at infinity.     

Theory of the influence of changes in salt concentration on the configuration of intrinsically curved, impenetrable, rod-like structures modeling DNA minicircles

DNA molecules in the familiar double helical B form are treated here as though they have rod-like structures obtained by stacking the nearly planar base pairs comprising them one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. As each base in a base pair is attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson-Crick structure, and each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair. Thus, each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to electrostatic forces, of sequentially remote origin, that, because they are only partially screened out by positively charged counter ions, can render the molecule's equilibrium configurations sensitive to changes in the concentration of salt in the medium. As there are cases in which, even though the intramolecular electrostatic forces of repulsion are strong, the distance of closest approach has value equal to that of the impenetrable diameter of the molecule, the theory presented here takes into account self-contact. Examples are given of cases in which the theory predicts that the radius of gyration of the minimum energy configuration of a small (549 base pair) circularized DNA molecule (called a “DNA minicircle”) has a remarkably strong dependence on the salt concentration.     

Structural changes in glutamate cell swelling followed by multiparametric q-space diffusion MR of excised rat spinal cord

Diffusion in the extracellular and intracellular spaces (ECS and ICS, respectively) was evaluated in excised spinal cords, before and after cell swelling induced by glutamate, by high b-value q-space diffusion MR of specific markers and water. The signal decays of deuterated tetramethylammonium (TMA-d(12)) chloride, an exogenous marker of the ECS, and N-acetyl aspartate (NAA), an endogenous marker of the ICS, were found to be non-mono-exponential at all diffusion times. The signal decays of these markers were found to depend on the diffusion time and the cell swelling induced by the glutamate. It was found, for example, that the mean displacements of the apparent fast and slow diffusion components of TMA-d(12) are 7.21 +/- 0.11 and 1.16 +/- 0.05 microm, respectively at a diffusion time of 496 ms. After exposure of the spinal cords to 10 mM of glutamate, these values decreased to 6.62 +/- 0.13 and 1.01 +/- 0.05 microm, respectively. The mean displacement of NAA, however, showed a less pronounced opposite trend and increased after cell swelling induced by exposure to glutamate. q-Space diffusion MR of water was found to be sensitive to exposure to glutamate, and q-space diffusion MRI showed that a more pronounced decrease in the apparent diffusion coefficient and the mean displacement of water is observed in the gray matter (GM) of the spinal cord. All these changes demonstrate that diffusion MR is indeed sensitive to structural changes caused by cell swelling induced by glutamate. Multiparametric high b-value q-space diffusion MR is useful for obtaining microstructural information in neuronal tissues.     

Sharp corners as sources of spiral pairs

It is demonstrated that using the FitzHugh-Nagumo model, stimulation of excitable media inside a region possessing sharp corners, can lead to the appearance of sources of spiral-pairs of sustained activity. The two conditions for such source creation are: The corners should be less than 120° and the range of stimulating amplitudes should be small, occurring just above the threshold value and decreasing with the corner angle. The basic mechanisms driving the phenomenon are discussed. These include: A. If the corner angle is below 120°, the wave generated inside cannot emerge at the corner tip, resulting in the creation of two free edges which start spiraling towards each other. B. Spiraling must be strong enough; otherwise annihilation of the rotating arms would occur too soon to create a viable source. C. The intricacies of the different radii involved are elucidated. Possible applications in heart stimulation and in chemical reactions are considered.     

Uniqueness results for quasilinear parabolic equations through viscosity solutions' methods

In this article, we are interested in uniqueness results for viscosity solutions of a general class of quasilinear, possibly degenerate, parabolic equations set in . Using classical viscosity solutions' methods, we obtain a general comparison result for solutions with polynomial growths but with a restriction on the growth of the initial data. The main application is the uniqueness of solutions for the mean curvature equation for graphs which was only known in the class of uniformly continuous functions. An application to the mean curvature flow is given.Received: 1 December 2001, Accepted: 30 September 2002, Published online: 17 December 2002Mathematics Subject Classification: 35A05, 35B05, 35D05, 35K15, 35K55, 53C44This work was partially supported by the TMR program "Viscosity solutions and their applications."