The FPU Problem as a Statistical-mechanical Counterpart of the KAM Problem,and Its Relevance for the Foundations of Physics

We give a review of the Fermi–Pasta–Ulam (FPU) problem from the perspective of its possible impact on the foundations of physics, concerning the relations between classical and quantum mechanics. In the first part we point out that the problem should be looked upon in a wide sense (whether the equilibrium Gibbs measure is attained) rather than in the original restricted sense (whether energy equipartition is attained). The second part is devoted to some very recent results of ours for an FPU-like model of an ionic crystal, which has such a realistic character as to reproduce in an impressively good way the experimental infrared spectra. Since the existence of sharp spectral lines is usually considered to be a characteristic quantum phenomenon, even unconceivable in a classical frame, this fact seems to support a thesis suggested by the original FPU result. Namely, that the relations between classical and quantum mechanics are much subtler than usually believed, and should perhaps be reconsidered under some new light.     

Simplicial complexes and Macaulay’s inverse systems

Let Δ be a simplicial complex on V = {x ₁, . . . , x _n }, with Stanley–Reisner ideal ${I_{\Delta}\subseteq R=k[x_1,\ldots, x_n]}Let Δ be a simplicial complex on V = {x ₁, . . . , x _n }, with Stanley–Reisner ideal I_D í R=k[x₁,?, x_n]{I_{\Delta}\subseteq R=k[x_1,\ldots, x_n]} . The goal of this paper is to investigate the class of artinian algebras A=A(D,a₁,?,a_n) = R/(I_D,x₁^a₁,?,x_n^a_n){A=A(\Delta,a_1,\ldots,a_n)= R/(I_{\Delta},x_1^{a_1},\ldots,x_n^{a_n})} , where each a _i ≥ 2. By utilizing the technique of Macaulay’s inverse systems, we can explicitly describe the socle of A in terms of Δ. As a consequence, we determine the simplicial complexes, that we will call levelable, for which there exists a tuple (a ₁, . . . , a _n ) such that A(Δ, a ₁, . . . , a _n ) is a level algebra.     

Extensions of a theorem of Cauchy-Liouville

We deal with the equations Δpu+f(u)=0 and Δpu+(p−1)g(u)p|∇u|+f(u)=0 in RN, where g(t) is a continuous function in (0,∞), p>1 and f(t) is a smooth function for t>0. Under appropriate conditions on g and f we show that the corresponding equation cannot have nontrivial non-negative entire solutions.     

A highly sensitive radial diffusion measurement method for white matter tract investigation

This article describes a novel approach for local estimation of the radial diffusion coefficient (D(perpendicular)) in white matter (WM) regions containing well-oriented nervous fibers. The method is based on the assumption that the diffusion process in well-organized WM regions responds to a cylindrical symmetry. The increased precision in the estimation of D(perpendicular) provided by this local approach compared to standard techniques based on diffusion tensor imaging is demonstrated using numerical simulations. An in vivo validation of the technique is also provided, showing its application to the corpus callosum of six healthy volunteers, highlighting the sensitivity of the method. Assuming that D(perpendicular) is sensitive to myelin integrity, our technique has the potential to investigate pathophysiological aspects of several neurological and psychiatric disorders with improved precision in targeted WM tracts.     

The longitudinal changes of BOLD response and cerebral hemodynamics from acute to subacute stroke. A fMRI and TCD study

Background  

By mapping the dynamics of brain reorganization, functional magnetic resonance imaging MRI (fMRI) has allowed for significant progress in understanding cerebral plasticity phenomena after a stroke. However, cerebro-vascular diseases can affect blood oxygen level dependent (BOLD) signal. Cerebral autoregulation is a primary function of cerebral hemodynamics, which allows to maintain a relatively constant blood flow despite changes in arterial blood pressure and perfusion pressure. Cerebral autoregulation is reported to become less effective in the early phases post-stroke.     

A new technique for the measurement of the product CO/CO2 ratio at the surface of char particles burning in a fluidized bed

A new experimental technique is proposed to measure the product CO/CO₂ ratio at the surface of spherical char particles during fluidized bed combustion. It is based on the measurement of the burning rate of a single char particle under low oxygen concentration conditions and on the use of an accurate prediction of the particle Sherwood number. This technique was applied to spherical char particles obtained from a bituminous coal which is characterized by a low attrition and fragmentation propensity. The product CO/CO₂ ratio was measured at a bed temperature of 850 °C and at a fluidization velocity of 0.3 m/s in a lab-scale apparatus operated with a bed of 0.5–0.6 mm sand. The char particle size was varied between 2 and 7 mm and the inlet oxygen concentration between 0.1% and 2.0%. Results showed that under the experimental conditions investigated carbon was mostly oxidized to CO₂ within the particle boundary layer, with a maximum fraction of carbon escaping as CO of 10–20% at the lowest oxygen concentrations and largest particle sizes.     

Chemical composition of the essential oil of Kaliphora madagascariensis Hook. f.

Kaliphora madagascariensis is an evergreen shrub or small tree endemic to Madagascar where it is traditionally used for the treatment of persistent cephalalgia by a strong inhalation of its odour. In this work, we analysed for the first time the essential oil obtained from leaves by Gas Chromatography-Mass Spectrometry. The chemical composition was dominated by oxygenated sesquiterpenes (68.1%), with caryophyllene oxide (14.7%) and β-eudesmol (10.7%) as the most abundant constituents. These compounds are endowed with documented healthy effects such as analgesic, anti-inflammatory, neuritogenic, antiepileptic and hypotensive, and its abundance might explain the traditional use of the plant in Madagascar.     

Hydrophobic siloxane paper coatings: the effect of increasing methyl substitution

Paper is an organic material widely used in cultural heritage and mainly composed of cellulose mixed with lignin, hemicellulose and small amounts of additives. This paper deals with siloxane coatings on pure cellulose paper, applied by sol–gel dipping in sols prepared with different siloxane precursors (tetraethoxysilane, methyl triethoxysilane, dimethyl diethoxysilane, trimethyl monoethoxysilane). The coated samples were characterized using various techniques (Fourier Transform Infrared Spectroscopy FT-IR, Nuclear Magnetic Resonance NMR and Scanning Electron Microscopy and Energy Dispersive Spectroscopy SEM–EDS), measuring their mechanical properties, flame resistance and contact angles, and a colorimetric test. The coated samples’ behavior was more hydrophobic the higher the methyl number of siloxane precursor, regardless of the coating’s thickness. Increasing the thickness improved the mechanical and thermal properties. The thickest coatings were obtained using a double coating process and a basic catalyst for the hydrolysis step, but this latter condition facilitated the formation of surface agglomerates, which make the paper too stiff and yellow.     

The (100), (111) and (110) surfaces of diamond: an ab initio B3LYP study

We present an accurate ab initio study of the structure and surface energy of the low-index (100), (111) and (110) diamond faces, by using the hybrid Hartree–Fock/density functional B3LYP Hamiltonian and a localised all-electron Gaussian-type basis set. A two-dimensional periodic slab model has been adopted, for which convergence on both structural and energetic parameters has been thoroughly investigated. For all the three surfaces, possible relaxations and reconstructions have been considered; a detailed geometrical characterisation is provided for the most stable structure of each orientation. Surface energy is discussed for all the investigated faces.