Electroweak quark-lepton symmetry and weak topological-charge confinement in the Standard Model with Dirac neutrinos

The standard electroweak model with Dirac neutrinos is extended by way of the principles of electroweak quark-lepton symmetry and weak topological-charge confinement to account for quark-lepton charge relations which, if not accidental, are indicative of charge structures. A mixing in quarks and leptons of underlying integer local charges with integer weak topological charges associated with an additive group Z_3, fixed by the anomaly cancellation requirement, is discussed. It is found that the electroweak difference between topological quarks and leptons is the nonequivalence between the topological vacua of their weak field configurations, produced by a four-instanton which carries the topological charge, induces the universal fractional piece of charge distinguishing quarks from leptons, and breaks the underlying symmetry. The constituent quarks of the standard model appear as coming from topological quarks, via the weak four-instanton event. Dual transitions occur for leptons. It is shown that several other fundamental problems left open in the standard electroweak model with Dirac neutrinos are solved: the one-to-one correspondence between quark and lepton flavors, the existence of three generations, the conservation and ungauging of B-L, the electric charge quantization, and the confinement of fractional electric charges.Comment: 23 pages, 1 figure, uses IJMPA.cl

Dynamics of shallow flows with and without background rotation

Large-scale oceanic and atmospheric flows tend to behave in a two-dimensional way. To further understand such flows, a large scientific effort has been devoted to the study of perfect two-dimensional flows. For the last 30 years, there has been a large interest in experimentally validating the results from numerical and theoretical studies concerning two-dimensional flows, particularly twodimensional turbulence and spatially periodic two-dimensional flows. Inspired by geophysical flows, experimentalists have used stratification, shallow fluid layer configurations, and background rotation to enforce the two-dimensionality of flows in the laboratory. However, as all these methods have shortcomings, it is difficult to achieve a perfectly two-dimensional flow in the laboratory. The work presented in this thesis focuses on two of the common methods used to enforce the two-dimensionality of flows: the shallow layer configuration and background rotation. To further understand the effect of these methods on the two-dimensionality of flows, we studied the dynamics of generic elementary vortical structures in a shallow fluid layer with and without background rotation. Through the analytical and numerical study of a decaying axisymmetric monopolar vortex, we revised the usual argument for considering shallow flowsas two-dimensional. This argument is based on the continuity equation, and it states that the vertical velocity can be neglected if the ratio of vertical to horizontal length scales of the flow is small. By performing numerical simulations and a perturbation analysis for shallow flows, it was shown that this argument is not valid in general, and that the two-dimensionality of the flow does not depend exclusively on the aspect ratio. Instead, it also depends on the dynamics of the flow; particularly, a shallow flow behaves in a two-dimensional way if the flow evolution is dominated by bottom friction over the whole fluid depth. These results were supported by the numerical and experimental study of a more complex flow structure, namely a dipolar vortex, in a shallow fluid layer. For the study of decaying dipolar vortices, numerical simulations were performed using a finite element code. The flow was initialized with a Lamb–Chaplygin dipolar vortex with a Poiseuille-like vertical profile, after which it was left to evolve freely. The 3D structure of the vortex was obtained using the 2 vortex detection criterion. Using this tool, it was observed how the vortex is gradually distorted due to the secondary 3D motions. An experimental investigation of an electromagnetically forced dipolar vortex, where Particle Image Velocimetry (PIV) was used to calculate the velocity field in a horizontal cross-section of the flow, supports the numerically obtained results. It is assumed that flows subjected to strong background rotation behave like two-dimensional flows due to the reduction of gradients in the direction parallel to the rotation axis, as stated by the Taylor–Proudman theorem. This phenomenon results in the formation of columnar structures. In the current work, it was found that the flow can behave in a two-dimensional way as long as the rotation rate is fast enough, irrespective of the aspect ratio. In other words, this is true even if the fluid depth is of the same order as the thickness of the Ekman boundary layer, for which case no columnar structures are formed. This is attributed to the linear coupling between primary and secondary motions. From the study of decaying vortical structures, it was concluded that neither adding background rotation to a shallow flow nor decreasing the depth of a rotating flow necessarily increases the degree of two-dimensionality of the flow. The last two chapters of this thesis are dedicated to the study of a shallow dipolar structure that is continuously driven by time-independent electromagnetic forcing. For a shallow structure without background rotation, it was observed that for weak forcing the flow can be considered indeed as twodimensional. However, every shallow flow, even for very small fluid depths, becomes three-dimensional for a sufficiently high forcing magnitude. An equivalent result was obtained for a similar flow subjected to background rotation. The change in behavior is associated with a change in the vertical profile of the horizontal velocity, which is clearly absent in perfectly two-dimensional flow. The results presented in this thesis confirm that under certain conditions shallow flows and flows subjected to background rotation can behave as a twodimensional flow. However, more importantly, it is shown that there are clear limits to this behavior. This work presents a better understanding of the basic dynamics of shallow flows with and without background rotation and of the extent to which these flows can be considered as quasi-two-dimensional

Photosynthesis of three dessert banana cultivars along an altitudinal gradient

Poster presented at Tropentag 2011 - Development on the Margin. Bonn (Germany), 3-7 Oct 2011

Exploiting Kronecker structure in exponential integrators: Fast approximation of the action of phi-functions of matrices via quadrature

In this article, we propose an algorithm for approximating the action of  $\varphi$-functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum structure, which arise from problems admitting a tensor product representation. The method is based on quadrature approximations of the integral form of the  $\varphi$-functions combined with a scaling and modified squaring method. Owing to the Kronecker sum representation, only actions of 1D matrix exponentials are needed at each quadrature node and assembly of the full matrix can be avoided. Additionally, we derive a priori bounds for the quadrature error, which show that, as expected by classical theory, the rate of convergence of our method is supergeometric. Guided by our analysis, we construct a fast and robust method for estimating the optimal scaling factor and number of quadrature nodes that minimizes the total cost for a prescribed error tolerance. We investigate the performance of our algorithm by solving several linear and semilinear time-dependent problems in 2D and 3D. The results show that our method is accurate and orders of magnitude faster than the current state-of-the-art

Determination of Benthic Soil Conditions Using Nematodes: Nematode FoodWeb Conditions of Fish Ponds in the Lincoln and Desha Counties of Arkansas

We determined the health status of similar channel catfish (Ictalurus punctatus) ponds in Lincoln and Desha counties of Arkansas, using the nematode soil food web condition as our reference point. Soil nematodes were categorized into colonizer-persister (cp) groups, based on their life course characteristics e.g sensitivity to environmental changes, body size, etc. These cp groups represent different components of the soil food web, which in turn were indicators of soil conditions. Benthic soil samples were collected at four week intervals over a 4-month period, from 6-ponds in each county. The nematodes were extracted according to standard methods and the recovered nematode taxa grouped according to their cp values. The product of each nematode taxon was determined (mean number of individuals x cp value) and the sum of all members of a cp group constituted the biomass produced by that cp group. Nematodes of the cp-3 and cp-4 groups dominated in biomass productivity in ponds for both counties. These groups of nematodes represent structured components of a food web and therefore a healthy ecosystem. Lincoln county ponds had higher cp-3 and cp-4 biomass likely due to slightly less acidic conditions while Desha county ponds had a greater biomass of plant-parasitic nematodes. It was also found that free-living nematodes tolerate more acidic conditions than plant-parasitic nematodes, though this could also be related to more root tissues. Nematode biomass calculations could be useful in determining benthic soil food web conditions, which may provide a simple way of assessing environmental conditions and changes in Arkansas catfish ponds

Techno-economic model and feasibility assessment of green hydrogen projects based on electrolysis supplied by photovoltaic PPAs

The use of hydrogen produced from renewable energy enables the reduction of greenhouse gas (GHG) emissions pursued in different international strategies. The use of power-purchase agreements (PPAs) to supply renewable electricity to hydrogen production plants is an approach that can improve the feasibility of projects. This paper presents a model applicable to hydrogen projects regarding the technical and economic perspective and applies it to the Spanish case, where pioneering projects are taking place via photovoltaic PPAs. The results show that PPAs are an enabling mechanism for sustaining green hydrogen projects

Exploiting the Kronecker product structure of φ−functions in exponential integrators

Exponential time integrators are well-established discretization methods for time semilinear systems of ordinary differential equations. These methods use (Formula presented.) functions, which are matrix functions related to the exponential. This work introduces an algorithm to speed up the computation of the (Formula presented.) function action over vectors for two-dimensional (2D) matrices expressed as a Kronecker sum. For that, we present an auxiliary exponential-related matrix function that we express using Kronecker products of one-dimensional matrices. We exploit state-of-the-art implementations of (Formula presented.) functions to compute this auxiliary function's action and then recover the original (Formula presented.) action by solving a Sylvester equation system. Our approach allows us to save memory and solve exponential integrators of 2D+time problems in a fraction of the time traditional methods need. We analyze the method's performance considering different linear operators and with the nonlinear 2D+time Allen–Cahn equation

Optimal dispatch model for PV-electrolysis plants in self-consumption regime to produce green hydrogen: a Spanish case study

The production of green hydrogen from renewable energy by means of water electrolysis is a promising approach to support energy sector decarbonization. This paper presents a techno-economic model of plants with PV sources connected to electrolysis in self-consumption regime that considers the dynamics of electrolysis systems. The model calculates the optimal hourly dispatch of the electrolysis system including the operational states (production, standby, and idle), the load factor in production, and the energy imports and exports to the electricity grid. Results indicate that the model is a useful decision support tool to operate electrolysis plants connected to PV plants in self-consumption regimes with the target of reducing hydrogen production costs

Pattern formation of spherical particles in an oscillating flow

We study the self-organization of spherical particles in an oscillating flow through experiments inside an oscillating box. The interactions between the particles and the time-averaged (steady streaming) flow lead to the formation of either one-particle-thick chains or multiple-particle-wide bands, depending on the oscillatory conditions. Both the chains and the bands are oriented perpendicular to the direction of oscillation with a regular spacing between them. For all our experiments, this spacing is only a function of the relative particle-fluid excursion length normalized by the particle diameter, $A_r/D$, implying that it is an intrinsic quantity that is established only by the hydrodynamics. In contrast, the width of the bands depends on both $A_r/D$ and the confinement, characterized by the particle coverage fraction $\phi$. Using the relation for the chain spacing, we accurately predict the transition from one-particle-thick chains to wider bands as a function of $\phi$ and $A_r/D$. Our experimental results are complemented with numerical simulations in which the flow around the particles is fully resolved. These simulations show that the regular chain spacing arises from the balance between long-range attractive and short-range repulsive hydrodynamic interactions, caused by the vortices in the steady streaming flow. We further show that these vortices induce an additional attractive interaction at very short range when $A_r/D\gtrsim0.7$, which stabilizes the multiple-particle-wide bands. Finally, we give a comprehensive overview of the parameter space where we illustrate the different regions using our experimental data.Comment: 20 pages, 16 figures, 1 table, to be submitted to Physical Review