A method of fundamental solutions for the one-dimensional inverse Stefan problem

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (-T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.

Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using a method of fundamental solutions

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional parabolic inverse Cauchy–Stefan problem, where boundary data and the initial condition are to be determined from the Cauchy data prescribed on a given moving interface. In [B.T. Johansson, D. Lesnic, and T. Reeve, A method of fundamental solutions for the one-dimensional inverse Stefan Problem, Appl. Math Model. 35 (2011), pp. 4367–4378], the inverse Stefan problem was considered, where only the boundary data is to be reconstructed on the fixed boundary. We extend the MFS proposed in Johansson et al. (2011) and show that the initial condition can also be simultaneously recovered, i.e. the MFS is appropriate for the inverse Cauchy-Stefan problem. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be efficiently obtained with small computational cost.

A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase inverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is more realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear combination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present situation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem is ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization needs to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are presented and discussed. © 2014 IMACS.

One-dimensional optical wave turbulence:experiment and theory

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Two-dimensional viscoelastic discrete triangular system with negative-stiffness components

Potential applications of high-damping and high-stiffness composites have motivated extensive research on the effects of negative-stiffness inclusions on the overall properties of composites. Recent theoretical advances have been based on the Hashin-Shtrikman composite models, one-dimensional discrete viscoelastic systems and a two-dimensional nested triangular viscoelastic network. In this paper, we further analyze the two-dimensional triangular structure containing pre-selected negative-stiffness components to study its underlying deformation mechanisms and stability. Major new findings are structure-deformation evolution with respect to the magnitude of negative stiffness under shear loading and the phenomena related to dissipation-induced destabilization and inertia-induced stabilization, according to Lyapunov stability analysis. The evolution shows strong correlations between stiffness anomalies and deformation modes. Our stability results reveal that stable damping peaks, i.e. stably extreme effective damping properties, are achievable under hydrostatic loading when the inertia is greater than a critical value. Moreover, destabilization induced by elemental damping is observed with the critical inertia. Regardless of elemental damping, when the inertia is less than the critical value, a weaker system instability is identified.

Crystal structure and physical properties of the new linear chain compound [Cu(1,2-bis(tetrazol-1-yl)ethane)3](ClO4)2

The synthesis and crystal structure of a novel one-dimensional Cu(II) compound [Cu(1,2-bis(tetrazol-1-yl)ethane)3](ClO4)2 are described. The single-crystal X-ray structure determination was carried out at 298 K. The molecular structure consists of a linear chain in which the Cu(II) ions are linked by three N4,N4' coordinating bis(tetrazole) ligands in syn conformation. The Cu(II) ions are in a Jahn-Teller distorted octahedral environment (Cu(1)-N(11)=2.034(2) Å, Cu(1)-N(21)=2.041(2) Å and Cu(1)-N(31)=2.391(2) Å). The Cu⋯Cu separations are 7.420(3) Å.

Toward the discovery of vaccine adjuvants:coupling in silico screening and in vitro analysis of antagonist binding to human and mouse CCR4 receptors

Background Adjuvants enhance or modify an immune response that is made to an antigen. An antagonist of the chemokine CCR4 receptor can display adjuvant-like properties by diminishing the ability of CD4+CD25+ regulatory T cells (Tregs) to down-regulate immune responses. Methodology Here, we have used protein modelling to create a plausible chemokine receptor model with the aim of using virtual screening to identify potential small molecule chemokine antagonists. A combination of homology modelling and molecular docking was used to create a model of the CCR4 receptor in order to investigate potential lead compounds that display antagonistic properties. Three-dimensional structure-based virtual screening of the CCR4 receptor identified 116 small molecules that were calculated to have a high affinity for the receptor; these were tested experimentally for CCR4 antagonism. Fifteen of these small molecules were shown to inhibit specifically CCR4-mediated cell migration, including that of CCR4+ Tregs. Significance Our CCR4 antagonists act as adjuvants augmenting human T cell proliferation in an in vitro immune response model and compound SP50 increases T cell and antibody responses in vivo when combined with vaccine antigens of Mycobacterium tuberculosis and Plasmodium yoelii in mice.

Random distributed feedback fibre laser

The concept of random lasers making use of multiple scattering in amplifying disordered media to generate coherent light has attracted a great deal of attention in recent years. Here, we demonstrate a fibre laser with a mirrorless open cavity that operates via Rayleigh scattering, amplified through the Raman effect. The fibre waveguide geometry provides transverse confinement and effectively one-dimensional random distributed feedback, leading to the generation of a stationary near-Gaussian beam with a narrow spectrum, and with efficiency and performance comparable to regular lasers. Rayleigh scattering due to inhomogeneities within the glass structure of the fibre is extremely weak, making the operation and properties of the proposed random distributed feedback lasers profoundly different from those of both traditional random lasers and conventional fibre lasers.

Development of novel NMR pulse sequences

To elucidate the structures of orgamc molecules in solution using pulse FT NMR, heteronuclear pulse sequence experiments to probe carbon-13 (13C) and proton (1H) spin systems are invaluable. The one-dimensional insensitive nucleus detected PENDANT experiment finds popular use for structure determination via one-bond 13C-1H scalar couplings. PENDANT facilitates the desired increase in 13C signal-to-noise ratio, and unlike many other pulse sequence experiments (e.g., refocused INEPT and DEPT), allows the simultaneous detection of 13C quaternary nuclei. The tlrst chapter herein details the characterisation of PENDANT and the successful rectification of spectral anomalies that occur when it is used without proton broadband decoupling. Multiple-bond (long-range) l3C-1H scalar coupling correlations can yield important bonding information. When the molecule under scrutiny is devoid of proton spectral crowding, and more sensitive 'inverse' pulse sequence experiments are not available, one may use insensitive nucleus detected long-range selective one-dimensional correlation methods, rather than more time consuming and insensitive multidimensional analogues. To this end a novel long-range selective one-dimensional correlation pulse sequence experiment has been invented. Based on PENDANT, the new experiment is shown to rival the popular selective INEPT technique because it can determine the same correlations while simultaneously detecting isolated 13C quaternary nuclei. INEPT cannot facilitate this, potentially leaving other important quaternary nuclei undetected. The novel sequence has been modified further to yield a second novel experiment that simultaneously yields selective 13C transient nOe data. Consequently, the need to perform the two experiments back-to-back is conveniently removed, and the experimental time reduced. Finally, the SNARE pulse sequence was further developed. SNARE facilitates the reduction of experimental time by accelerating the relaxation of protons upon which pulse sequences, to which SNARE is appended, relies. It is shown, contrary to the original publication, that reiaxation time savings can be derived from negative nOes.

Molecular architecture influences on material properties of pharmaceutical compounds

Salt formation has extensively been studied as a strategy to improve drug solubility but it has not been explored as a strategy to improve mechanical properties. A better understanding of which factors of the solid state can have an influence in the mechanical properties of pharmaceutical powders can help to optimise and reduce cost of tablet manufacturing. The aim of this study was to form different series of amine salts of flurbiprofen, gemfibrozil and diclofenac and to establish predictive relationships between architectural characteristics and physicochemical and mechanical properties of the salts. For this purpose, three different carboxylic acid drugs were selected: flurbiprofen, gemfibrozil and diclofenac, similar in size but varying in flexibility and shape and three different series of counterions were also chosen: one with increasing bulk and no hydroxyl groups to limit the hydrogen bonding potential; a second one with increasing number of hydroxyl groups and finally a third series, related to the latter in number of hydroxyl groups but with different molecular shape and flexibility. Physico-chemical characterization was performed (DSC, TGA, solubility, intrinsic dissolution rate, particle size, true density) and mechanical properties measured using a compaction replicator. Strained molecular conformations produce weaker compacts as they have higher energy than preferred conformations that usually lie close to energy minimums and oppose plastic deformation. It was observed that slip planes, which correspond to regions of weakest interaction between the planes, were associated with improved plasticity and stronger compacts. Apart from hydrogen bonds, profuse van der Waals forces can result in ineffective slip planes. Salts displaying two-dimensional densely hydrogen bonded layers produced stronger compacts than salts showing one-dimensional networks of non-bonded columns, probably by reducing the attachment energy between layers. When hydrogen bonds are created intramolecularly, it is possible that the mechanical properties are compromised as they do not contribute so much to create twodimensional densely bonded layers and they can force molecules into strained conformations. Some types of hydrogen bonding network may be associated with improved mechanical properties, such as type II, or R (10) 3 4 using graph-set notation, versus type III, or R (12) 4 8 , columns. This work clearly demonstrates the potential of investigating crystal structure-mechanical property relationship in pharmaceutical materials.

A method of fundamental solutions for two-dimensional heat conduction

We investigate an application of the method of fundamental solutions (MFS) to heat conduction in two-dimensional bodies, where the thermal diffusivity is piecewise constant. We extend the MFS proposed in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction, Eng. Anal. Bound. Elem. 32 (2008), pp. 697–703] for one-dimensional heat conduction with the sources placed outside the space domain of interest, to the two-dimensional setting. Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate results can be obtained efficiently with small computational cost.