Quantitative MRS study of Baló's concentric sclerosis lesions

Baló's concentric sclerosis (BCS) lesions display specific metabolite changes detected by magnetic resonance spectroscopy (MRS). We report on two cases of BCS lesions examined by MRS; the first case was evaluated 36 days after the onset of symptoms, whereas the second case was evaluated 9 days after the onset of symptoms. MRS data were obtained from single voxels located in the lesion and in the contralateral region. Relative to the creatine/phosphocreatine peak, BCS lesions displayed decreases of N-acetyl aspartate and increases of choline, myo-inositol (mI), glutamine/glutamate (Glx), lactate and lipid+macromolecule signals, in agreement with previous reports. In addition, previously unreported decreases of mI (-19% to -29%) and increases of Glx (+55% to +198%) were measured; these could be useful in characterizing BCS lesions.     

Spin hamiltonian for which the chiral spin liquid is the exact ground state

We construct a Hamiltonian that singles out the chiral spin liquid on a square lattice with periodic boundary conditions as the exact and, apart from the twofold topological degeneracy, unique ground state.     

Algebraic classification of Weyl anomalies in arbitrary dimensions

Conformally invariant systems involving only dimensionless parameters are known to describe particle physics at very high energy. In the presence of an external gravitational field, the conformal symmetry may generalize to the Weyl invariance of classical massless field systems in interaction with gravity. In the quantum theory, the latter symmetry no longer survives: A Weyl anomaly appears. Anomalies are a cornerstone of quantum field theory, and, for the first time, a general, purely algebraic understanding of the universal structure of the Weyl anomalies is obtained, in arbitrary dimensions and independently of any regularization scheme.     

On Infinitesimal Shear

The setting for this note is the theory of infinitesimal strain in the context of classical linearized elasticity. As a body is subjected to a deformation the angle between a pair of material line elements through a typical point P is changed. The decrease in angle is called the shear of this pair of elements. Here, we determine all pairs of material line elements at P which are unsheared in a deformation. It is seen, in general, that corresponding to any given material line element in a given plane through P, there is one corresponding “companion” material line element such that the given element and its conjugate are unsheared in the deformation. There are two exceptions. If the plane through P is a plane of central circular section of the strain ellipsoid, then every material line element through P in this plane has an infinity of companion elements in this plane – all pairs of material line elements in the plane(s) of central circular section of the strain ellipsoid are unsheared. If the plane through P is not a plane of central circular section of the strain ellipsoid, then there are two exceptional material line elements through P such that neither of them has a companion material line element forming an unsheared pair with it. The directions of these exceptional elements in the plane are called “limiting directions”. It is seen that it is the pair of elements along the limiting directions in a plane which suffer the maximum shear in that plane. A geometrical construction is presented for the determination of the extensional strains along the pairs of elements which are unsheared. Also, it is shown that knowing one unsheared pair in a plane and their extensions is sufficient to determine the principal extensions and the principal axes in this plane. Expressions for all unsheared pairs in a given plane are given in terms of the normals to the planes of central circular sections of the strain ellipsoid. Finally, for a given material line element, a formula is derived for the determination of all other material line elements which form an unsheared pair with the given element.     

Innovative high-performance liquid chromatography method development for the screening of 19 antimalarial drugs based on a generic approach, using design of experiments, independent component analysis and design space

An innovative methodology based on design of experiments (DoE), independent component analysis (ICA) and design space (DS) was developed in previous works and was tested out with a mixture of 19 antimalarial drugs. This global LC method development methodology (i.e. DoE-ICA-DS) was used to optimize the separation of 19 antimalarial drugs to obtain a screening method. DoE-ICA-DS methodology is fully compliant with the current trend of quality by design. DoE was used to define the set of experiments to model the retention times at the beginning, the apex and the end of each peak. Furthermore, ICA was used to numerically separate coeluting peaks and estimate their unbiased retention times. Gradient time, temperature and pH were selected as the factors of a full factorial design. These retention times were modelled by stepwise multiple linear regressions. A recently introduced critical quality attribute, namely the separation criterion (S), was also used to assess the quality of separations rather than using the resolution. Furthermore, the resulting mathematical models were also studied from a chromatographic point of view to understand and investigate the chromatographic behaviour of each compound. Good adequacies were found between the mathematical models and the expected chromatographic behaviours predicted by chromatographic theory. Finally, focusing at quality risk management, the DS was computed as the multidimensional subspace where the probability for the separation criterion to lie in acceptance limits was higher than a defined quality level. The DS was computed propagating the prediction error from the modelled responses to the quality criterion using Monte Carlo simulations. DoE-ICA-DS allowed encountering optimal operating conditions to obtain a robust screening method for the 19 considered antimalarial drugs in the framework of the fight against counterfeit medicines. Moreover and only on the basis of the same data set, a dedicated method for the determination of three antimalarial compounds in a pharmaceutical formulation was optimized to demonstrate both the efficiency and flexibility of the methodology proposed in the present study.     

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is approximated by lower-dimensional objects, and a hyperviscous term is added to the flow equation. The hyperviscosity is given by the product of the ordinary viscosity with the square of a length that is shown to play the role of effective thickness of any lower-dimensional object. Explicit solutions of simple problems illustrate how the proposed method is able to represent with good approximation both the velocity field and the drag forces generated by rigid motions of the immersed bodies, in analogy with classical slender-body theories. This approach has the potential to open up the way to more effective computational techniques, since geometrical complexities can be significantly reduced. This, however, is achieved at the expense of involving higher-order derivatives of the velocity field. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.     

On Deformations with the Same Principal Stretches

In the context of the finite strain theory, plane isochoric homogeneous deformations are considered. Inspired by two examples (plane elliptical and plane hyperbolic deformations), it is seen that for any such isochoric deformation the corresponding principal stretches are equal to those of simple shear provided there is a certain relation between the amount of shear of the simple shear and the parameters of the general plane deformation. Then, the link is established between any two homogeneous deformations which have identical principal stretches. It involves two rotations, one in the undeformed state and the other in the deformed state. These rotations are determined explicitly for an arbitrary isochoric homogeneous deformation and the simple shear with the same principal stretches.     

Sharp-crack limit of a phase-field model for brittle fracture

A matched asymptotic analysis is used to establish the correspondence between an appropriately scaled version of the governing equations of a phase-field model for fracture and the equations of the two-dimensional sharp-crack theory of Gurtin and Podio-Guidugli (1996) that arise on assuming that the bulk constitutive behavior is nonlinearly elastic, requiring that surface energy provides the only factor limiting crack propagation, and assuming that the fracture kinetics are isotropic. Consistent with the prominence of the configurational momentum balance at the crack tip in the latter theory, the approach capitalizes on the configurational momentum balance that arises naturally in the context of the phase-field model. The model developed and utilized here incorporates irreversibility of the phase-field evolution. This is achieved by introducing a suitable constraint and by carefully heeding the influence of that constraint on the kinetics underlying microstructural changes associated with fracture. The analysis is predicated on the assumption that the phase-field variable takes values in the closed interval between zero and unity.