A mean-field monomer-dimer model with attractive interaction. The exact solution

A mean-field monomer-dimer model which includes an attractive interaction among both monomers and dimers is introduced and its exact solution rigorously derived. The Heilmann-Lieb method for the pure hard-core interacting case is used to compute upper and lower bounds for the pressure. The bounds are shown to coincide in the thermodynamic limit for a suitable choice of the monomer density m. The consistency equation characterising m is studied in the phase space (h, J), where h tunes the monomer potential and J the attractive potential. The critical point and exponents are computed and show that the model is in the mean-field ferromagnetic universality class.Comment: 32 pages, 6 figure

Interaction mechanisms and damage formation in laser cutting of CFRP laminates obtained by recycled carbon fibre

The increase in the use of composite materials poses the problem of their disposal/recycling after the End of Life (EOL). Different strategies were developed to recycle composite material, resulting in the availability of new raw materials, characterised by overall good mechanical properties and significantly low cost. However, the applicability of these materials to industrial production also depends on the possibility of producing and processing them with likewise available technologies. Among the production and processing technologies that can be adopted for recycled composite materials, resin infusion under flexible tooling (RIFT) and laser machining, respectively, stand out above all due to the high production/machining speed compared to the cost. This paper investigates the possibility to apply both these technologies to carbon fibre-reinforced polymer laminates obtained by adopting recycled carbon fibres. Recycled CFRP plates of about 2.7 mm in thickness were produced by RIFT and characterised in tensile and flexural tests. After mechanical characterisation, cutting tests were performed by using a 450 W QCW fibre laser, varying the pulse power, the pulse length, and the pulse overlap. The kerf geometries and the HAZ extension were measured at the upper and bottom parts as well as in the section. Analysis of variance was adopted to define which and how the process parameters affect the kerf dimension and HAZ extension. Results showed that it is possible to cut the composite at a cutting speed up to 2000 mm/s, obtaining, in the best conditions, narrow kerf, limited HAZ, and taper angle of about 0 degrees

Evaluation of the effects of the metal foams geometrical features on thermal and fluid-dynamical behavior in forced convection

Metal foams are a material, featuring interesting characteristics for the aeronautical and automotive fields because of their low specific weight, high thermal properties, and mechanical performances. In particular, this paper deals with thermal and fluid dynamic study of 24 open-cell aluminum EN43500 (AlSi10MnMg) metal foams produced by indirect additive manufacturing (I-AM), combining 3D printing and metal casting to obtain a controllable morphology. A study of foam behavior function of the morphological features (pores per inch (PPI), branch thickness (r), and edges morphology (smooth-regular)) was performed. The samples produced were heated by radiation and tested in an open wind circuit gallery to measure the fluid dynamic properties such as pressure drop (Delta p), inertial coefficient (f), and permeability (k), in an air forced convection flow. The thermal characterization was performed evaluating both the theoretical (k(th)) and effective (k(eff)) thermal conductivity of the foams. Also, the global heat transfer coefficient (HTCglobal) was evaluated with different airflow rates. Analysis of variance (ANoVA) was performed to figure out which geometrical parameters are significant during both thermal and fluid dynamic processes. The results obtained show how the controllable foam morphology can affect the involved parameters, leading to an ad hoc design for industrial applications that require high thermo-fluid-dynamical performances

The Solution of the Deep Boltzmann Machine on the Nishimori Line

The deep Boltzmann machine on the Nishimori line with a finite number of layers is exactly solved by a theorem that expresses its pressure through a finite dimensional variational problem of min–max type. In the absence of magnetic fields the order parameter is shown to exhibit a phase transition whose dependence on the geometry of the system is investigated

Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Cystic Fibrosis Defective Response to Infection Involves Autophagy and Lipid Metabolism

Cystic fibrosis (CF) is a hereditary disease, with 70% of patients developing a proteinopathy related to the deletion of phenylalanine 508. CF is associated with multiple organ dysfunction, chronic inflammation, and recurrent lung infections. CF is characterized by defective autophagy, lipid metabolism, and immune response. Intracellular lipid accumulation favors microbial infection, and autophagy deficiency impairs internalized pathogen clearance. Myriocin, an inhibitor of sphingolipid synthesis, significantly reduces inflammation, promotes microbial clearance in the lungs, and induces autophagy and lipid oxidation. RNA-seq was performed in Aspergillusfumigatus-infected and myriocin-treated CF patients' derived monocytes and in a CF bronchial epithelial cell line. Fungal clearance was also evaluated in CF monocytes. Myriocin enhanced CF patients' monocytes killing of A. fumigatus. CF patients' monocytes and cell line responded to infection with a profound transcriptional change; myriocin regulates genes that are involved in inflammation, autophagy, lipid storage, and metabolism, including histones and heat shock proteins whose activity is related to the response to infection. We conclude that the regulation of sphingolipid synthesis induces a metabolism drift by promoting autophagy and lipid consumption. This process is driven by a transcriptional program that corrects part of the differences between CF and control samples, therefore ameliorating the infection response and pathogen clearance in the CF cell line and in CF peripheral blood monocytes

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

Second-order L2L^2-regularity in nonlinear elliptic problems

A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the existence and square integrability of the weak derivatives of the nonlinear expression of the gradient under the divergence operator. This provides a nonlinear counterpart of the classical $L^2$-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are established. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required. If the domain is convex, no regularity of its boundary is needed at all

Estudio de factores pronósticos en el tratamiento de la carcinomatosis mucinosa peritoneal de origen apendicular mediante citorreducción y quimioterapia intraperitoneal hipertérmica (HIPEC)

Las neoplasias apendiculares son poco frecuentes, suponen el 0,4% de los tumores gastrointestinales, presentan una incidencia de 0,12 casos por 100.000 habitantes-año y cuentan con un amplio espectro histológico. Los tumores epiteliales mucinosos de origen apendicular son característicamente muy proclives a la diseminación por vía peritoneal dando lugar a la denominada Carcinomatosis Mucinosa Peritoneal de Origen Apendicular (CMPOA), objeto de estudio de este trabajo. Desde las primeras descripciones histológicas ha existido un intenso debate en cuanto a su nomenclatura que persiste hasta nuestros días, además, existen distintas clasificaciones histológicas con mayor o menor aceptación que han dificultado la estandarización de los términos en torno a la CMPOA. En la actualidad sigue pendiente la creación de una clasificación de consenso universalmente aplicable. La historia natural de la CMPOA se caracteriza por la liberación de moco y células tumorales epiteliales libres desde el apéndice a la cavidad peritoneal, éstas se van a diseminar al resto de la cavidad siguiendo caminos predefinidos según el “fenómeno de redistribución” descrito por Sugarbaker, depositándose con mayor probabilidad en lugares específicos como son los diafragmas, el omento mayor, la región ileocecal, el rectosigma y la pelvis. Inicialmente el paciente se mantendrá asintomático o con sintomatología limitada, sin embargo con el avance de la enfermedad, el material mucinoso abarcará toda la cavidad peritoneal conduciendo a un estado de caquexia y obstrucción intestinal. El método diagnóstico de elección de la CMPOA es el TC con contraste iv..