Application of the sequential gradient-restoration algorithm to thermal convective instability problems

The problem of the thermal stability of a horizontal incompressible fluid layer with linear and nonlinear temperature distributions is solved by using the sequential gradient-restoration algorithm developed for optimal control problems. The hydrodynamic boundary conditions for the layer include a rigid or free upper surface and a rigid lower surface. The resulting disturbing equations are solved as a Bolza problem in the calculus of variations. The results of the study are compared with the existing works in the literature.The authors acknowledge valuable discussions with Dr. A. Miele.     

Dissipation functions and conservation laws of molecular liquids and solids

Thermodynamics of molecular liquids (anisotropic liquids, liquid crystals, etc.) and molecular solids (e.g. dielectrics, pyroelectrics, molecular crystals) are treated in a unified way, using an internal energy potentialU and a dissipation functionD. Assuming that the motion of the mass points making up the molecule is essential in determiningU we write down the appropriate field equations of motion and the entropy equation. With the assumed invariance ofU under a group of space-time transformations and the invariance ofD under rigid body uniform motions, we derive the conservation laws of mass, momentum, energy and angular momentum. In particular, we show that the total stress tensor is asymmetric.Furthermore, a symmetric stress tensor does not guarantee angular momentum conservation. The complete specification ofD leads to symmetry relations between the dissipative coefficients in an unambiguous way, without invoking the concept of so called forces and fluxes, in contrast to the conventional Onsager approach. Our formalism allows for a class of different dissipation functions, and is applicable to linear or nonlinear molecular media of arbitrary symmetry. It covers simple materials as special cases.     

Dynamics of viscous fingers in Hele-Shaw cells of liquid crystals Theory and experiment

The theoretical and experimental developments in the interfacial dynamics and the formation of viscous fingering patterns in Hele-Shaw cells of liquid crystal-air systems are summarized and discussed. These include radial and linear cells with or without grooves engraved on the cell plates. Instabilities of fingers, the role of intrinsic and extrinsic anisotropies, etc., are emphasized. In a linear cell, when the injected air is kept at constant pressure, a whole sequence of successive instabilities of fingers (hump, tip-splitting, sidewrinkling, sidebranching and DLA-like structure) is observed in a single run of the experiment. In our theory, the equations of motion of nematic flows in Hele-Shaw cells are derived from the Ericksen-Leslie equations. In the linear approximation, the equations resemble those of isotropic liquids with the presence of effective viscosities and anisotropic surface tension. Experimental observations are interpreted with the introduction of an effective control parameter which may be time dependent. Special features of viscous fingers in liquid crystals in contrast to those in isotropic liquids, such as asymmetric dendritics, displacement of the finger from the central axis of the linear cell, and reentrant sequence of patterns, are pointed out. Plausible explanations of these phenomena are given. In this newly developed field, a large number of interesting problems remain to be solved.     

Extremal loading of soft fibrous tissues: multi-scale mechanics and constitutive modeling

In the current contribution, we present a multi-scale constitutive model capturing macroscopic inelastic effects (like stress softening and permanent set) in soft tissues under cyclic loading. Soft biological tissues can be described as a biological composite material. The extracellular matrix is hereby reinforced by collagen fibers which themself are an assembly of collagen fibrils embedded in a proteoglycan (PG) rich matrix. Micro-damage induced by cyclic loading is treated by an interaction scenario between the fibrils and the PGs. At the low strain regime PGs promote sliding between fibrils [1] which leads to the yielding of statistical distributed overlapping segments. The breakage of the PG-bridges is defined by a decreasing PG-density. Due to the accumulated damage of the PG connections at high tissue strains, the strains at the fibril level increases. This finally drives the over-stretching of the fibrils, which is associated with a permanent rupture of the hydrogen bonds inside of the tropocollagen molecules [2]. The so obtained model is in line with recent experimental findings [1, 2] and was additionally validated against experimental data available in literature. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Improved Stabilities of Labeling Probes for the Selective Modification of Endogenous Proteins in Living Cells and In Vivo

To date, various affinity-based protein labeling probes have been developed and applied in biological research to modify endogenous proteins in cell lysates and on the cell surface. However, the reactive groups on the labeling probes are also the cause of probe instability and nonselective labeling in a more complex environment, e. g., intracellular and in vivo. Here, we show that labeling probes composed of a sterically stabilized difluorophenyl pivalate can achieve efficient and selective labeling of endogenous proteins on the cell surface, inside living cells and in vivo. As compared with the existing protein labeling probes, probes with the difluorophenyl pivalate exhibit several advantages, including long-term stability in stock solutions, resistance to enzymatic hydrolysis and can be customized easily with diverse fluorophores and protein ligands. With this probe design, endogenous hypoxia biomarker in living cells and nude mice were successfully labeled and validated by in vivo, ex vivo, and immunohistochemistry imaging.     

Evidence for Electron Transfer between Graphene and Non-Covalently Bound π-Systems

Hybridizing graphene and molecules possess a high potential for developing materials for new applications. However, new methods to characterize such hybrids must be developed. Herein, the wet-chemical non-covalent functionalization of graphene with cationic π-systems is presented and the interaction between graphene and the molecules is characterized in detail. A series of tricationic benzimidazolium salts with various steric demand and counterions was synthesized, characterized and used for the fabrication of graphene hybrids. Subsequently, the doping effects were studied. The molecules are adsorbed onto graphene and studied by Raman spectroscopy, XPS as well as ToF-SIMS. The charged π-systems show a p-doping effect on the underlying graphene. Consequently, the tricationic molecules are reduced through a partial electron transfer process from graphene, a process which is accompanied by the loss of counterions. DFT calculations support this hypothesis and the strong p-doping could be confirmed in fabricated monolayer graphene/hybrid FET devices. The results are the basis to develop sensor applications, which are based on analyte/molecule interactions and effects on doping.     

On the embedding of graphs into graphs with few eigenvalues

A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic graphs of type k for every k ≥ 3. Furthermore, in the case k ≥ 5 such a family of extensions can be found at every sufficiently large order. Some bounds for the extension will also be given. © 1996 John Wiley & Sons, Inc.     

Modeling of interphase in composite materials: Characterization of epoxy resin/aminosilane system

The system studied here principally is γ-APS + BADGE (γ-aminopropyltriethoxysilane + diglycidyl ether of bisphenol A). The reaction takes place even at −20°C. It is first the epoxy-amine autocatalytic second-order reaction, but we also have a cross-linking reaction which needs more time and higher temperature. The behaviour of this system is the same as γ-APS-PGE (phenylglycidyl ether) system: we can obtain the complete disappearance of OH groups. The thermomechanical properties of the reaction product considerably change with the temperature, moisture and curing time.     

Discovery of an NAD+ analogue with enhanced specificity for PARP1

Among various protein posttranslational modifiers, poly-ADP-ribose polymerase 1 (PARP1) is a key player for regulating numerous cellular processes and events through enzymatic attachments of target proteins with ADP-ribose units donated by nicotinamide adenine dinucleotide (NAD⁺). Human PARP1 is involved in the pathogenesis and progression of many diseases. PARP1 inhibitors have received approvals for cancer treatment. Despite these successes, our understanding about PARP1 remains limited, partially due to the presence of various ADP-ribosylation reactions catalyzed by other PARPs and their overlapped cellular functions. Here we report a synthetic NAD⁺ featuring an adenosyl 3′-azido substitution. Acting as an ADP-ribose donor with high activity and specificity for human PARP1, this compound enables labelling and profiling of possible protein substrates of endogenous PARP1. It provides a unique and valuable tool for studying PARP1 in biology and pathology and may shed light on the development of PARP isoform-specific modulators.

An analogue of nicotinamide adenine dinucleotide (NAD⁺) featuring an azido group at 3′-OH of adenosine moiety is found to possess high specificity for human PARP1-catalyzed protein poly-ADP-ribosylation.