Imprisoned lightning: charge transport in trehalose-derived sugar glasses

Trehalose is a naturally occurring disaccharide noted for its ability to preserve the biological function of proteins and cell membranes during periods of stress—such as water deprivation or extreme temperature—by stabilizing the conformations of the macromolecules within a glassy matrix. This phenomenon makes use of the propensity for trehalose to interact strongly with protein functional groups and solvent water molecules via hydrogen bonding. Previously, it has been shown that trehalose sugar glasses also support long-range charge transport in oxidation-reduction reactions occurring between spatially separated donors and acceptors. Here, through the use of bulk Arrhenius DC-conductivity measurements, we infer that this anomalously high carrier mobility is due to proton hopping along a hydrogen bonding network formed by sorbed “water wires,” a process known as the Grotthuss mechanism. Additionally, we find that the apparent activation energy of the conductivity depends non-monotonically on the bias voltage. The possibility is raised for novel photovoltaic devices based on the entrapment of photosynthetic proteins within these glasses.     

Cardinal characteristics at κ in a small u(κ) model

We provide a model where $\mathfrak{u}(\kappa )<2^{\kappa }$ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.     

Reconstruction of large coherent structures from SPIV measurements in a forced turbulent mixing layer

A procedure is suggested here for reconstructing the time variation of a three-dimensional (3D) coherent velocity field, based on applying Least Square Method to a very limited number of phase-locked measurements. The measurements are performed in a spanwise plane of a forced turbulent mixing layer by employing the stereo particle image velocimetry system. The forcing is produced by oscillating two- and three-dimensional (3D) flappers placed at the edge of the splitter plate. The feasibility and validity of the procedure for velocity field reconstruction are checked by using Hot Wire Measurements. Very clear patterns are observed of two types of coherent structures: spanwise K-H billows (rolls) and streamwise vortices. These are due to primary and secondary instabilities and their time evolution is presented.     

Inverse problems for scattering by periodic structures

Suppose the 3-dimensional space is filled with three materials having dielectric constants ? ₁ above S ₁={x ₂=f ₁(x ₁), x ₃ arbitrary}, ? ₂ below S ₂ = {x ₂ =f ₂(x ₁), x ₃ arbitrary} and ? _o in {f ₂(x ₁) <x ₂ 1(x ₁), x ₃ arbitrary} where f ₁ f ₂ are periodic functions. Suppose for a plane wave incident on S ₁ from above we can measure the reflected and transmitted waves of the corresponding time-harmonic solution of the Maxwell equations, say at x ₂=±b,b large. To what extent can we infer from these measurements the location of the pair (S ₁, S ₂ ? In this paper, we establish a local stability: If ( $\tilde S_1 ,\tilde S_2$ ) is another pair of periodic curves “close” to (S ₁, S₂), then, for any δ>0, if the measurements for the two pairs are δ-close, then $\tilde S_1$ and $\tilde S_2$ are 0(δ)-close to S ₁ and S ₂, respectively.     

Uniform Convergence for Approximate Traveling Waves in Linear Reaction–Diffusion–Hyperbolic Systems

In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p ₀ = p ₀(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons. The matrix (k _ij ) is assumed to have a unique null vector with positive components summed to 1 and the v _j are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α.     

Cup and cap products in intersection (co)homology

We construct cup and cap products in intersection (co)homology with field coefficients. The existence of the cap product allows us to give a new proof of Poincaré duality in intersection (co)homology which is similar in spirit to the usual proof for ordinary (co)homology of manifolds.