Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Schatten properties,nuclearity and minimality of phase shift invariant spaces

We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator $\mathrm{Op}(a)$ is a Schatten-q operator from $M^{\infty }$ to $M^p$ and r-nuclear operator from $M^{\infty }$ to $M^r$ when $a\in M^r$ for suitable p, q and r in $(0,\infty ]$.     

α-Diphenylphosphino-N-(pyrazin-2-yl)glycine as a ligand in Ni-catalyzed ethylene oligomerization

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Backstepping-based output regulation for systems with infinite-dimensional actuator and sensor dynamics

The output regulation problem is solved for an ODE plant driven by a parabolic actuator with spatially varying coefficients. Applying the backstepping transformation to the actuator allows the solution of the regulator equations in closed-form and thus the formulation of the solvability condition. An output feedback regulator is obtained by designing a disturbance observer using delayed measurement and a reference observer that both achieve finite-time convergence. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Novel Dithiolene Complexes and Tetrathiafulvalenes

Abstract

Novel dithiolene metal complexes, some of which absorb in the near infrared, and tetrathiafulvalenes, in particular tetraiodotetrathia- fulvalene, have been prepared, and their magnetic properties studied.     

Complementary MS Methods Assist Conformational Characterization of Antibodies with Altered S–S Bonding Networks

As therapeutic monoclonal antibodies (mAbs) become a major focus in biotechnology and a source of the next-generation drugs, new analytical methods or combination methods are needed for monitoring changes in higher order structure and effects of post-translational modifications. The complexity of these molecules and their vulnerability to structural change provide a serious challenge. We describe here the use of complementary mass spectrometry methods that not only characterize mutant mAbs but also may provide a general framework for characterizing higher order structure of other protein therapeutics and biosimilars. To frame the challenge, we selected members of the IgG2 subclass that have distinct disulfide isomeric structures as a model to evaluate an overall approach that uses ion mobility, top-down MS sequencing, and protein footprinting in the form of fast photochemical oxidation of proteins (FPOP). These three methods are rapid, sensitive, respond to subtle changes in conformation of Cys?→?Ser mutants of an IgG2, each representing a single disulfide isoform, and may be used in series to probe higher order structure. The outcome suggests that this approach of using various methods in combination can assist the development and quality control of protein therapeutics.      

APplication of Continuous Thermodynamics to the Stability of Polymer Systems. II

A determinant criterion for the critical state in solutions and mixtures of polydisperse polymers is established within the general framework of Gibbs theory. The treatment continues an earlier paper by considering more general Gibbs free energy relations: The function replacing the x-term in the classic Flory-Huggins equation is permitted to depend on a finite number of moments of the polymer distribution(s) so as to embrace most Gibbs free energy relations of practical use. The new criterion leads to a very large reduction of computer time and of needed storage capacity compared to the traditional Gibbs determinant criterion. Some relations known from the literature are shown to be special cases of the established new criterion.     

Equilibrium Topology and Partial Inversion of Janus Drops: A Numerical Analysis

The equilibrium topology of an aqueous Janus emulsion of two oils, O1 and O2, with water, W, [(O1+O2)/W], is numerically evaluated with the following realistic interfacial tensions (γ): γ_O2/W=5 mN m⁻¹, γ_O1/O2=1 mN m⁻¹, and γ_O1/W varies within the range 4–5 mN m⁻¹, which is the limiting range for stable Janus drop topology. The relative significance of the two independently pivotal factors for the topology is evaluated, that is, the local equilibrium at the line of contact between the three liquids and the volume fraction of the two dispersed liquids within the drop. The results reveal a dominant effect of the local equilibrium on the fraction of the O2 drop surface that is covered by O1. In contrast, for a constant volume of O2, the impact of the interfacial tension balance on the limit of the coverage is modest for an infinite volume of O1. Interestingly, when the O1 volume exceeds this value, an emulsion inversion occurs, and the O1 portion of the (O1+O2)/W topology becomes a continuous phase, generating a (W+O2)/O1 Janus configuration.     

Arraying Cell Cultures Using PEG‐DMA Micromolding in Standard Culture Dishes

A robust and effortless procedure is presented, which allows for the microstructuring of standard cell culture dishes. Cell adhesion and proliferation are controlled by three‐dimensional poly(ethylene glycol)‐dimethacrylate (PEG‐DMA) microstructures. The spacing between microwells can be extended to millimeter size in order to enable the combination with robotic workstations. Cell arrays of microcolonies can be studied under boundary‐free growth conditions by lift‐off of the PEG‐DMA layer in which the growth rate is accessible via the evolution of patch areas. Alternatively, PEG‐DMA stencils can be used as templates for plasma‐induced patterning.