Study of the atom-phonon coupling model for (SC) partition function: first order phase transition for an infinite linear chain

In spin-conversion (SC) compounds containing molecules organized around an iron (II) ion the fundamental level of the ion is low spin (LS), S = 0, and its first excited one is high spin (HS), S = 2. This energy diagram is due to the ligands field interaction on 3d electrons and to the spin pairing energy. Heating the compound increases the magnetic susceptibility which corresponds to a change of populations of both levels and consequently a change of spin value of the molecules. This mechanism, called spin conversion (SC), can be accompagnied by thermal hysteresis observed by studying magnetic susceptibility or high spin fraction. In that case one considers that the (SC) takes place through a first-order phase transition due to intermolecular interactions. In the atom-phonon coupling model the molecules are considered as two-level systems, or two-level atoms, and it is assumed that the elastic force constant value of the spring which links two atoms first neighbours is depending on the electronic states of both atoms. In this study we calculate the partition function of a linear chain of N atoms (N ≤ 16) and we describe the role of phonons and that of the parameter Δ which corresponds to the distance in energy between both levels. The chain free-energy function is F _atph . We introduce for the chain a free-energy function defined by the set (F _HS , F _LS , F _barr ) and we show that F _atph tends towards the previous set when N → ∞. The previous set allows to describe a first order phase transition between a (LS) phase and a (HS) one. At the crossing point between the function F _LS and F _HS , and around this point, there is an intermediate free-energy barrier which prevents the chain to change phase which can lead to thermal hysteresis. The energy gap between the free-energy function F _atph and that defined by the set (F _HS , F _LS , F _barr ) is small. So we can expect that a nanoparticule takes for free-energy function that defined by the set and then displays a thermal hysteresis.     

Krein’s Theorems for a Dissipative Boundary Value Transmission Problem

Let us consider the differential expression $$\ell (y)=-y^{\prime \prime }+q(x)y,\quad x\in I:=[0,c)\cup (c,\infty ),$$ where c is a transmission point and is regular for the differential expression ?(y). We assume that Weyl’s limit-circle case holds for the differential expression ?(y) on I. In this paper, using Krein’s theorems, we investigate the completeness of the root vectors of a singular dissipative boundary value transmission problem generated by ?(y).     

Supramolecular hydrogels formed by pyrene-terminated poly(ethylene glycol) star polymers through inclusion complexation of pyrene dimers with γ-cyclodextrin

Novel supramolecular hydrogels were formed between pyrene-terminated poly(ethylene glycol) star polymers and γ-cyclodextrin (γ-CD), through the inclusion complexation of dimers of the pyrene terminals with γ-CD, where γ-CD was directly used as a supramolecular cross-linking reagent without any modification.     

Towards modelling skeletal muscle growth and adaptation

Despite an increasing interest in modelling skeletal muscles adaptation, models that address the phenomena within a continuum-mechanical framework using muscle-specific material models are rare in literature. This work focuses on modelling one form of skeletal musle adaptation, namely sarcomerogenesis. Sarcomerogenesis occurs when a given stretch is sustained over a period of time and the number of basic contractile units, which are the sarcomeres, increase. To model sarcomerogenesis within a continuum-mechanical setting, the growth framework based on a multiplicative split of the total deformation gradient is employed. An evolution equation that describes sarcomerogenesis is used and incorporated in a transversally isotropic material model that accounts for a skeletal muscle's active force production capabilities. The material tangent modulus is derived and implemented within the finite-element analysis software. Using this model, one sees that increased number of sarcomeres results in a decreased force response of the muscle tissue over time. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dissipative operators with impulsive conditions

In this paper a singular dissipative impulsive boundary value problem with $n$ -impulsive points is investigated. In particular, using the Lidski?’s theorem it is proved that all eigen and associated functions of this problem is complete in the Hilbert space.     

Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale

We review some of the recent advances in the development of subwavelength plasmonic devices for manipulating light at the nanoseale, drawing examples from our own work in metal-dielectric-metal （MDM） plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switching in MDM plasmonic waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced.     

Thin-film polymerization and characterization of Sumitomo's Sumikasuper®-type liquid crystalline polymers

Using the thin film polymerization approach, we have studied the texture evolution when synthesizing a novel liquid crystalline polymer (LCP) system based on Sumikasuper^® LCPs. The main monomers used were p-acetoxybenzoic acid (ABA), 4,4'-biphenol (BP), isophthalic acid (IA), phthalic acid (PA) and terephthalic acid (TA). Polarizing optical microscopy (POM), FTIR, X-ray diffraction (XRD) and atomic force microscopy (AFM) were employed to study the thin film polymerization process and characterize the products. The generation and evolution of liquid crystal phases were monitored; the results revealed that there exists a composition range for the monomers to react and form liquid crystal materials. The critical temperature for LC formation in ABA/BP/IA system decreased with increasing ABA content. FTIR results confirmed the formation of polymers. AFM investigation suggested a similar process of morphological change to that observed using POM. An increasing surface roughness of the thin films with the progress of polymerization was also obtained from AFM analysis. A nematic LC texture of the polymer system was suggested by XRD examination. Results obtained by replacing BP with acetylated BP, and by conducting polymerization using two-monomer systems, suggest that BP units are included in polymers obtained by the thin film polymerization method.     

Krein's Theorem for the Dissipative Operators with Finite Impulsive Effects

In this article, singular dissipative operators with finite impulsive conditions are investigated. In particular, after passing to the inverse operators, it is obtained that the imaginary parts of the inverse operators are nuclear. Finally, using Krein's theorem, it is proved that all root vectors of the singular dissipative operators with finite impulsive conditions are complete in the Hilbert space.     

On the eigenvalues of second-order boundary-value problems

In this paper we investigate the properties of eigenvalues of some boundary-value problems generated by second-order Sturm-Liouville equation with distributional potentials and suitable boundary conditions. Moreover, we share a necessary condition for the problem to have an infinitely many eigenvalues. Finally, we introduce some ordinary and Frechet derivatives of the eigenvalues with respect to some elements of the data.