A geometrical analysis of the field equations in field theory

In this review paper we give a geometrical formulation of the field equations in the Lagrangian and Hamiltonian formalisms of classical field theories (of first order) in terms of multivector fields. This formulation enables us to discuss the existence and non-uniqueness of solutions, as well as their integrability.Comment: 14 pages. LaTeX file. This is a review paper based on previous works by the same author

Multi-probe analysis of the galaxy cluster CL J1226.9+3332: Hydrostatic mass and hydrostatic-To-lensing bias

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAMThe precise estimation of the mass of galaxy clusters is a major issue for cosmology. Large galaxy cluster surveys rely on scaling laws that relate cluster observables to their masses. From the high-resolution observations of ∼45 galaxy clusters with the NIKA2 and XMM-Newton instruments, the NIKA2 Sunyaev-Zela'dovich Large Program should provide an accurate scaling relation between the thermal Sunyaev-Zela'dovich effect and the hydrostatic mass. In this paper we present an exhaustive analysis of the hydrostatic mass of the well-known galaxy cluster CL J1226.9+3332, the highest-redshift cluster in the NIKA2 Sunyaev-Zela'dovich Large Program at z=0.89. We combined the NIKA2 observations with thermal Sunyaev-Zela'dovich data from the NIKA, Bolocam, and MUSTANG instruments and XMM-Newton X-ray observations, and tested the impact of the systematic effects on the mass reconstruction. We conclude that slight differences in the shape of the mass profile can be crucial when defining the integrated mass at R500, which demonstrates the importance of the modelling in the mass determination. We prove the robustness of our hydrostatic mass estimates by showing the agreement with all the results found in the literature. Another key factor for cosmology is the bias of the masses estimated assuming the hydrostatic equilibrium hypothesis. Based on the lensing convergence maps from the Cluster Lensing And Supernova survey with Hubble (CLASH) data, we obtain the lensing mass estimate for CL J1226.9+3332. From this we are able to measure the hydrostatic-To-lensing mass bias for this cluster, which spans from 1-bHSE/lens∼0.7 to 1, presenting the impact of data sets and mass reconstruction models on the bia

Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

Respuesta de las variaciones del nivel medio diario del mar en el Caño de Sancti Petri (Cádiz, España)

Sea level series were recorded from October 2006 to January 2007 at two different sites in a shallow-water estuary of SW Spain. Results showed a very significant temporal variability in daily sea level. Moreover, 85% of the variance was explained by atmospheric pressure variability, obtaining a relation between sea level and atmospheric pressure of around –2 cm hPa–1. A more detailed study showed the existence of two different types of oscillations in daily sea level: the first, with periods of 10 days, was related to the inverted barometer (IB) effect associated with synoptic-scale atmospheric pressure oscillations (IB factor of around 1.4 ± 0.1 cm hPa–1), and the second, with periods of more than 10 days, was related to pressure changes in the planetaryscale atmospheric waves. Even though the high barometric behaviour of the 10-day period was partially related to the local winds, the shallowness of the study area invalidated the assumption of a static IB effect (–1 cm hPa–1). Rather, it was the dynamic IB effect that explained the displacement of the IB factor relative to the static assumption.Se analizaron dos series simultáneas del nivel del mar registradas entre octubre de 2006 y enero de 2007 en una zona estuarina somera al sur de España. Los resultados evidenciaron una variabilidad temporal muy significativa del nivel medio diario del mar. Del análisis de las series se dedujo que 85% de la varianza es explicada por variaciones de la presión atmosférica, con un factor de proporcionalidad entre ambas series en torno a –2 cm hPa–1. Un estudio más exhaustivo demostró la existencia de dos tipos de oscilación en el nivel medio diario del mar, uno con periodos en torno a los 10 días cuyo comportamiento fue explicado por el efecto de barómetro invertido originado por las oscilaciones de presión atmosférica de escala sinóptica, con valores de factor de barómetro invertido (BI) en torno a –1.4 ± 0.1 cm hPa–1, y otro con periodos superiores a 10 días, asociado a las variaciones de presión atmosférica ligadas a las ondas atmosféricas de escala planetaria. Aunque el efecto local del viento permitió explicar una pequeña parte del comportamiento supra-barométrico observado, la poca profundidad de la zona de estudio hizo que la suposición de efecto de BI estático (–1 cm hPa–1) dejase de tener validez en esta zona, siendo el efecto de barómetro invertido dinámico el que permitió explicar las desviaciones del FBI respecto a la esperada respuesta estática

On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial).Comment: 25 page

Biobased polymers derived from itaconic acid bearing clickable groups with potent antibacterial activity and negligible hemolytic activity.

Herein, we report, for the first time, the synthesis of clickable polymers derived from biobased itaconic acid, which was then used for the preparation of novel cationic polymers with antibacterial properties and low hemotoxicity via click chemistry. Itaconic acid (IA) was subjected to chemical modification by incorporating clickable alkyne groups on the carboxylic acids. The resulting monomer with pendant alkyne groups was easily polymerized and copolymerized with dimethyl itaconate (DMI) by radical polymerization. The feed molar ratio of comonomers was varied to precisely tune the content of alkyne groups in the copolymers and the amphiphilic balance. Subsequently, an azide with a thiazole group, which is a component of the vitamin thiamine (B1), was attached onto the polymers by copper-catalyzed azidealkyne cycloaddition (CuAAC) click chemistry leading to triazole linkages. N-Alkylation reactions of the thiazole and triazole groups with methyl and butyl iodides provide the corresponding itaconate derivatives with pendant azolium groups. The copolymers with variable cationic charge densities and hydrophobic/ hydrophilic balances, depending on the comonomer feed ratio, display potent antibacterial activity against Gram-positive bacteria, whereas the activity was almost null against Gram-negative bacteria. Hemotoxicity assays demonstrated that the copolymers exhibited negligible hemolysis and excellent selectivity, more than 1000-fold, for Gram-positive bacteria over human red blood cells.post-print1945 K

PLA and PBAT-based electrospun fibers functionalized with antibacterial bio-based polymers

Antimicrobial fibers based on biodegradable polymers, poly(lactic acid) (PLA), and poly(butylene adipate-co-terephthalate) (PBAT) are prepared by electrospinning. For this purpose, a biodegradable/bio-based polyitaconate containing azoles groups (PTTI) is incorporated at 10 wt.% into the electrospinning formulations. The resulting fibers functionalized with azole moieties are uniform and free of beads. Then, the accessible azole groups are subjected to N-alkylation, treatment that provides cationic azolium groups with antibacterial activity at the surface of fibers. The positive charge density, roughness, and wettability of the cationic fibers are evaluated and compared with flat films. It is confirmed that these parameters exert an important effect on the antimicrobial properties, as well as the length of the alkylating agent and the hydrophobicity of the matrix. The quaternized PLA/PTTI fibers exhibit the highest efficiency against the tested bacteria, yielding a 4-Log reduction against S. aureus and 1.7-Log against MRSA. Then, biocompatibility and bioactivity of the fibers are evaluated in terms of adhesion, morphology and viability of fibroblasts. The results show no cytotoxic effect of the samples, however, a cytostatic effect is appreciated, which is ascribed to the strong electrostatic interactions between the positive charge at the fiber surface and the negative charge of the cell membranes

On some aspects of the geometry of differential equations in physics

In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular differential equations, and partial differential equations in field theories. The geometric structures underlying these systems are presented and commented. The main results concerning these structures are stated and discussed, as well as their influence on the study of the differential equations with which they are related. Furthermore, research to be developed in these areas is also commented.Comment: 21 page