Homogenization of layered elastoplastic composites: Theoretical results

Exact closed-form solutions are derived that completely characterize the effective behavior of a composite material made of elastic-perfectly plastic parallel plane layers perfectly bonded together. The derivation is framed within a rigorous theory of homogenization for elastoplastic composites, and based on the fundamental fact that the in-plane part of the strain tensor and the out-of-plane part of the stress tensor are uniform throughout the composite provided no free-edge effects occur. The obtained expressions are coordinate-free and valid in the general anisotropic case. As an example, a layered composite material with isotropic constituents is examined in detail.     

Rate dependence of temperature fields and energy dissipations in non-static pseudoelasticity

The temperature fields and the energy dissipations of shape memory alloys during the stress-induced martensitic transformations are studied theoretically and experimentally. The effect of the loading rate is analyzed. It was found that the temperature field inside a shape memory alloy sample varies strongly in space and time. The increase rate of the temperature is given by the difference between the rate of the latent heat release and the rate of the heat convection and conduction. The notion and the rate dependence of the energy dissipation are discussed in connection with the stress–strain hysteresis, the entropy production, and the Clausius–Duhem inequality.     

On the Hamming distances of repeated-root constacyclic codes of length 4ps

Let $p$ be an odd prime, $s$, $m$ be positive integers, $\gamma ,\lambda$ be nonzero elements of the finite field ${\mathbb{F}}_{p^m}$ such that ${\gamma }^{p^s}=\lambda$. In this paper, we show that, for any positive integer $\eta$, the Hamming distances of all repeated-root $\lambda$-constacyclic codes of length $\eta p^s$ can be determined by those of certain simple-root $\gamma$-constacyclic codes of length $\eta$. Using this result, Hamming distances of all constacyclic codes of length $4p^s$ are obtained. As an application, we identify all MDS $\lambda$-constacyclic codes of length $4p^s$.     

Interlaced solitons and vortices in coupled DNLS lattices

In the present work, we propose a new set of coherent structures that arise in nonlinear dynamical lattices with more than one component, namely interlaced solitons. In the anti-continuum limit of uncoupled sites, these are waveforms whose one component has support where the other component does not. We illustrate systematically how one can combine dynamically stable unary patterns to create stable ones for the binary case of two-components. For the one-dimensional setting, we provide a detailed theoretical analysis of the existence and stability of these waveforms, while in higher dimensions, where such analytical computations are far more involved, we resort to corresponding numerical computations. Lastly, we perform direct numerical simulations to showcase how these structures break up, when they are exponentially or oscillatorily unstable, to structures with a smaller number of participating sites.     

Hydrothermal synthesis and structural characterization of a one-dimensional coordination polymer [Zn(Pydc)(Dppz)] n (H2Pydc = 2,6-pyridinedicarboxylic acid, Dppz = dipyrido[3,2-a:2′,3′-c]phenazine)

A new metal-organic coordination polymer [Zn(Pydc)(Dppz)] _n (I) (H₂Pydc = 2,6-pyridinedicarboxylic acid, Dppz = dipyrido[3,2-a:2′,3′-c]phenazine) was hydrothermally synthesized and characterized by elemental analysis, IR and X-ray single-crystal diffraction. The X-ray diffraction analysis reveals that I crystallizes in the monoclinic system, space group P2₁/c. The Pydc^2? ligands adopt O,N,O′-tridentate chelating and monodentate bridging coordination mode to link two adjacent Zn2+ ions to form a one-dimensional (1D) zigzag chain. The adjacent chains are further linked through hydrogen bonds and π-π stacking interactions, forming a three-dimensional (3D) supramolecular framework. The unit cell parameters for I: a = 7.332(3) Å, b = 36.023(9) Å, c = 7.8838(13) Å, β = 105.65(3)^○, V = 2005.1(10) ų, Z = 4.     

Methyl (E)-2-(2-phenylcyclopropylidene)acetate: Synthesis, isomerization, and reaction with 1,3-diphenyl-2-benzofuran

Treatment of 3-methyl-2-phenylcycloprop-2-ene-1-carboxylic acid with potassium tert-butoxide induced its isomerization into trans-2-methylidene-3-phenylcyclopropane-1-carboxylic acid which was converted into methyl ester, and heating of the latter for 1 h in toluene gave methyl (E)-2-(2-phenylcyclopropylidene)acetate. Thermal isomerization of methyl (E)-2-(2-phenylcyclopropylidene)acetate on prolonged heating in toluene afforded 5-methoxy-3-methyl-2-phenylfuran, and the reaction with 1,3-diphenyl-2-benzofuran resulted in [4 + 2]-cycloaddition at the exocyclic double bond.     

Composition heterogeneity of tetrafluoroethylene-hexafluoropropylene random copolymers characterized by successive self-nucleation and annealing

In the present work, successive self-nucleation and annealing (SSA) was applied to a series of tetrafluoroethylene-hexafluoropropylene random copolymers (FEPs). Multiple melting peaks were observed for all FEP samples after SSA thermal treatment. The lamellar crystal thicknesses were calculated from the melting temperatures, and the mass percentages of the crystals of specific thickness were obtained from the areas of the melting peaks. As a result, distributions of the lamellar thickness, which can be correlated to the composition distribution, were determined. It was found that the composition distribution of the FEP samples tended to become more heterogeneous as the content of hexafluoropropylene (HFP) comonomer increases. Samples with the same HFP content might also have different composition distributions.     

Design of Sensitive Biocompatible Quantum‐Dots Embedded in Mesoporous Silica Microspheres for the Quantitative Immunoassay of Human Immunodeficiency Virus‐1 Antibodies

A novel sandwich‐type electrochemiluminescence (ECL) immunosensor was developed to enable the sensitive detection of HIV‐1 antibodies. This system incorporated mesoporous silica (mSiO₂) complexed with quantum dots (QDs) and nano‐gold particles, which were assembled to enhance signal detection. Magnetic beads were used by immobilizing the secondary anti‐IgG antibody. This was first employed to capture HIV‐1 antibody (Ab) to form a Fe₃O₄/anti‐IgG/Ab complex. A high loading and signal‐enhanced nanocomposite (hereafter referred to as Au‐mSiO₂‐CdTe) was used as a HIV‐1 antigen label. The Au‐mSiO₂‐CdTe nanocomposite was conjugated with the Fe₃O₄/anti‐IgG/Ab complex to form an immunocomplex (hereafter referred to as Fe₃O₄/anti‐IgG/Ab/HIV‐1/CdTe‐mSiO₂‐Au). This complex could be further separated by an external magnetic field to produce ECL signals. Due to the large specific surface area and pore volume of mSiO₂, the loading of the CdTe QDs was markedly increased. Thus, the loaded QDs released a powerful chemiluminescent signal with a concordantly increased sensitivity of the immunosensor. The immunosensor was highly sensitive, and displayed a linear range of responses for HIV‐1 antibody across a dilution range of 1 : 1500 through 1 : 50 with the detection limit of 1 : 4500. The immunoassay can be a promising candidate in early diagnosis of HIV infection.     

Process-directed self-assembly of multiblock copolymers: Solvent casting <Emphasis Type="Italic">vs</Emphasis> spray coating

Using computer simulation of a soft, coarse-grained model and self-consistent field theory we investigate how collapsed, globular chain conformations in the initial stages of structure formation, which are produced by spray-coating, affect the single-chain structure and morphology of microphase-separated multiblock copolymers. Comparing spray-coated films with films that start from a disordered state of Gaussian chains, we observe that the collapsed molecular conformations in the initial stage give rise to (1) a smaller fraction of blocks that straddle domains (bridges), (2) a significant reduction of the molecular extension normal to the internal interfaces, and (3) a slightly larger lamellar domain spacing in the final morphology. The relaxation of molecular conformations towards equilibrium is very protracted for both processes – solvent casting and spray coating. These findings illustrate that the process conditions of the copolymer materials may significantly affect materials properties (such as mechanical properties) because the system does not reach thermal equilibrium on the relevant time scales.