Synthesis and characterization of a chiral antiferroelectric series with new SmC A*-L transition

Two new chiral series with a tolane core: (S) 4-(1-methylheptyloxycarbonyl)phenyl (series IB) and (S) 4-(1-ethylheptyloxycarbonyl)phenyl (series IC) 4-alkanoyloxytolane-4'-carboxylates have been synthesized and characterized. All the compounds are mesomorphic, and most of them display the antiferroelectric SmC*A phase. The mesomorphic properties have been analysed by optical microscopy, DSC, helical pitch and electro-optical measurements and X-ray diffraction study. Series IB exhibits a very rich polymesomorphism with SmC*alpha, SmC*, SmC* F12, SmC* F11 and SmC*A phases, like the previously reported series IA, [(S) 4-(1-methylheptyloxycarbonyl)phenyl 4-alkyloxytolane-4-carboxylates]. Series IC is more interesting because it presents for the first time in antiferroelectric series the liquid-like phase (L phase) between the SmC*A and isotropic phases. Preliminary optical studies plead in favour of a helical short range structure for this new liquid-like L phase.     

Energy Scaling Laws for Conically Constrained Thin Elastic Sheets

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h|logh|, where h?1 is the thickness of the sheet, we establish matching upper and lower bounds of order h ²|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.     

Key properties of monohalogen substituted phenols: interpretation in terms of the electron localization function

This paper is an attempt to bridge the key properties of monohalogen substituted phenols with the electronic localization function, which has a vivid 3D topological pattern and the vector gradient field of which is determined by the electron transition current density. A primary goal is to interpret the ‘anomalous’ strength of the intramolecular hydrogen bond O—H···X formed in cis ortho-X substituted phenols, depending upon the halogen atom (X = F, Cl, and Br) in terms of the populations of the electronic localization function basins and a so-called core valence bifurcation index. A theoretical model is considered aiming to explain convincingly the cis-trans conversion in ortho-X phenols occurring in some solvents and resulting in the experimentally observed splitting of the ν_OH stretch and based on the Pauling model. Characteristic harmonic vibrational modes of all monohalogen substituted phenols are discussed thoroughly. The order of stability of monohalogen substituted phenols is established at a high level of computational performance, showing the ‘anomalous’ order of stability of fluorophenols, the result being that, in contrast to Cl and Br, the F atom favours the trans meta position over the cis ortho with formation of the intramolecular hydrogen bond.     

Synthesis,properties and crystal structure of chiral semiperfluorinated liquid crystals with ferro and anticlinic smectic phases

A new chiral and semiperfluorinated series with ferro and anticlinic properties has been synthesized and characterized. The mesomorphic behaviour has been established on the grounds of both microscopic observations and DSC measurements. The non-chiral intermediate ethyl 4-semiperfluorinated alkyloxybenzoates exhibit SmA phases, unusual for compounds with a single phenyl ring. The final derivatives display SmA, SmC* and in several cases SmC*A phases. The longer fluorinated chains favour the SmA and SmC* phases at the expense of the SmC*A phase. Electro-optical measurements were carried out with the classical SSFLC geometry. The spontaneous polarization and tilt angle at saturation are higher than those of the hydrogenous homologues, around 140 nCcm-2 at 40 degrees C. One compound of the series, the 4,4,5,5,6,6,7,7,8,8,8-nonafluoroheptyloxy derivative, C36H35O7F9, Mx=750.6 g mol-1, crystallizes in the triclinic system, space group P1 with four independent molecules in the asymmetric unit (Z=4). The molecules are arranged in a head-to-tail fashion with two molecules oriented in the same direction and the two others in the opposite direction. They give rise to sheets with a smectic C-like arrangement. The final reliability factors were R=0.117 and wR=0.134; the goodness of fit was S=1.366.     

Discreteness of interior transmission eigenvalues revisited

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the multiplier technique and the second one is based on the Fourier analysis. The key point of the analysis is to establish the compactness and the uniqueness for Cauchy problems under various conditions. Using these approaches, we are able to rediscover quite a few known discreteness results in the literature and obtain various new results for which only the information near the boundary are required and there might be no contrast of the coefficients on the boundary.     

BIOECONOMIC MODEL OF EASTERN BALTIC COD UNDER THE INFLUENCE OF NUTRIENT ENRICHMENT

Abstract The objective of this paper is to study the economic management of Eastern Baltic cod (Gadus morhua) under the influence of nutrient enrichment. Average nitrogen concentration in the spawning areas during the spawning season of cod stock is chosen to be an indicator of nutrient enrichment. The optimal cod stock is defined using a dynamic bioeconomic model for the cod fisheries. The results show that the current stock level is about half of the estimated optimal stock level and that the current total allowable catch (TAC) is about one‐fourth of the optimal equilibrium yield. The results also indicate that the benefit from a reduction in nitrogen very much depends on the harvest policies. If the TAC is set equal to the optimal equilibrium yield, the benefit of a nitrogen reduction from the 2009 level to the optimal nitrogen level would be about 604 million DKK over a 10‐year time horizon, given a discount rate of 4% per year. However, if a recovery management plan is chosen, the benefit would only be about 49 million DKK over a 10‐year time horizon.     

Analysis of a Compressed Thin Film Bonded to a Compliant Substrate: The Energy Scaling Law

We consider the deformation of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit is far beyond critical. We take a variational viewpoint—focusing on the total elastic energy, i.e. the membrane and bending energy of the film plus the elastic energy of the substrate—viewing the buckling of the film as a problem of energy-driven pattern formation. We identify the scaling law of the minimum energy with respect to the physical parameters of the problem, and we prove that a herringbone pattern achieves the optimal scaling. These results complement previous numerical studies, which have shown that an optimized herringbone pattern has lower energy than a number of other patterns. Our results are different, because (i) we make the scaling law achieved by the herringbone pattern explicit, and (ii) we give an elementary, ansatz-free proof that no pattern can achieve a better law.     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.     

A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity

We revisit the asymptotic formulas originally derived in [D.J. Cedio-Fengya, S. Moskow, M.S. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems 14 (1998) 553–595; A. Friedman, M. Vogelius, Identification of small inhomogeneities of extreme conductivity by boundary measurements: A theorem on continuous dependence, Arch. Ration. Mech. Anal. 105 (1989) 299–326]. These formulas concern the perturbation in the voltage potential caused by the presence of diametrically small conductivity inhomogeneities. We significantly extend the validity of the previously derived formulas, by showing that they are asymptotically correct, uniformly with respect to the conductivity of the inhomogeneities. We also extend the earlier formulas by allowing the conductivities of the inhomogeneities to be completely arbitrary L^∞$L^{\infty }$, positive definite, symmetric matrix-valued functions. We briefly discuss the relevance of the uniform asymptotic validity, and the admission of arbitrary anisotropically conducting inhomogeneities, as far as applications of the perturbation formulas to “approximate cloaking” are concerned.     

Photodiode-Based Chua＇s Circuit with Light Controllability

We present a photodiode-based Chua＇s chaotic circuit that is controllable by light. The proposed circuit consists of an inductor, two passive capacitors, a photodiode-based variable resistor, and a positive feedback trans- conductor with negative nonlinearity. The chaotic dynamics of the circuit were verified by using the simulation program with integrated circuit emphasis analysis using the 0.35 #m complementary metal-oxide-semiconductor process parameters. The gain results （such as the time waveform~ frequency analysis, three-dimensional attractor, bifurcation and Lyapunov exponents diagrams） confirm that the chaotic behavior of the circuit could be controlled by light intensity via the photodiode-based variable resistor.