arXiv subjects

Pablo Padilla

Publications and source records attributed to Pablo Padilla.

28 records · Page 2Linked to original sources

arXiv2021

Cross-polarization Control in FSSs by means of an Equivalent Circuit Approach

This paper presents an efficient equivalent circuit approach (ECA), based on a Floquet modal expansion, for the study of the co- and cross-polarization in frequency selective surfaces (FSS) formed by periodic arrays of patches/apertures in either single or stacked configurations. The ECA makes it possible the derivation of analytical expressions for the generalized scattering parameters associated with the proposed circuit networks. Furthermore, the proposed circuit approach is an efficient surrogate model that can be combined with optimization techniques and artificial intelligence algorithms for the efficient design of FSS structures, saving efforts in the computation compared to time-consuming full-wave simulators and tedious synthesis (simulation-assisted) techniques. Due to the simplicity of the topology of the involved networks, the ECA can also be advantageously used to gain physical insight. The proposed approach is applied and validated in different FSS configurations where the cross-pol component plays a fundamental role in the design, as in circular polarizers, polarization rotators, and reflectarray cells.

physics.app-ph↗

arXiv2021

Generalized Director Approach for Liquid-Crystal-Based Reconfigurable RF Devices

This letter presents a closed-form integral-equation formulation that models the director tilting in nematic liquid crystals. The proposed formulation is computationally efficient compared to numerical methods and provides a physical insight on the matter. Our previous work is generalized from the one-constant approach to all the possible cases that cover the elastic constants. These constants determine in great extent the electrical properties of the liquid crystal, and subsequently, the response of the reconfigurable devices that take use of it. Therefore, a more precise but still simple modeling of their influence is pursued here. Simulations show good agreement with numerical implementations. In comparison, the error in the estimation is considerably reduced when using the integral-equation formulation, specially as the polarization voltage or the dielectric anisotropy decreases.

cond-mat.soft↗

arXiv2021

Exploring the Potentials of the Multi-modal Equivalent Circuit Approach for Stacks of 2-D Aperture Arrays

Many frequency selective surface (FSS) structures are based on the use of a single periodic array of slot/apertures in a conducting sheet embedded in a layered medium. However, it is well known that stacking several conducting sheets and breaking the alignment of the stack can bring multiple benefits to the structure. In this paper, the analysis and design of stacks of 2-D aperture arrays are carried out by exploiting as much as possible all the potentialities of a rigorous and systematic formulation based on the multi-modal equivalent circuit approach (ECA). A key feature of the formulation is that linear transformations between the apertures of adjacent plates (rotation, translation, and scaling) can be dealt with from a purely analytical perspective. This fact is of potential interest for many practical applications, such as the design of polarization converters, absorbers, filters, and thin matching layers. When the apertures have an arbitrary geometry, it can be applied a hybrid approach that combines the ability of commercial simulators to handle arbitrary geometries with the fast computation times and physical insight of the ECA. In general, either the purely analytical or the hybrid approach can be applied in those many practical scenarios where the spatial profile of the electric field on the considered apertures hardly changes with frequency. As an additional feature of the approach, the dispersion properties (phase/attenuation constants and Bloch impedance) of infinite periodic stacks can be derived and, in particular, analytical expressions for mirror- and glide-symmetric configurations are provided.

physics.app-ph↗

arXiv2021

Glide-Symmetric Metallic Structures with Elliptical Holes for Lens Compression

In this paper, we study the wave propagation in a metallic parallel-plate structure with glide-symmetric elliptical holes. To perform this study, we derived a mode-matching technique based on the generalized Floquet theorem for glide-symmetric structures. This mode-matching technique benefits from a lower computational cost since it takes advantage of the glide symmetry in the structure. It also provides physical insight on the specific properties of Floquet modes propagating in these specific structures. With our analysis, we demonstrate that glide-symmetric structures with periodic elliptical holes exhibit an anisotropic refractive index over a wide range of frequencies. The equivalent refractive index can be controlled by tuning the dimensions of the holes. Finally, by combining the anisotropy related to the elliptical holes and transformation optics, a Maxwell fish-eye lens with a 33.33% size compression is designed. This lens operates in a wideband frequency range from 2.5 GHz to 10 GHz.

physics.app-ph↗

arXiv2021

Dispersion and Filtering Properties of Rectangular Waveguides Loaded With Holey Structures

This paper analyzes thoroughly the dispersion and filtering features of periodic holey waveguides in the millimeter-wave frequency range. Two structures are mainly studied depending on the glide and mirror symmetries of the holes. A parametric study of the dispersion characteristics of their unit cells is carried out. Glide-symmetric holey waveguides provide a higher propagation constant and a low dispersion over a wide frequency range regarding hollow waveguides. This property is particularly useful for the design of low-loss and low-dispersive phase shifters. We also demonstrate that glide-symmetric holey waveguides are less dispersive than waveguides loaded with glide-symmetric pins. Furthermore, we perform a Bloch analysis to compute the attenuation constants in holey waveguides with mirror and broken glide symmetries. Both configurations are demonstrated to be suitable for filter design. Finally, the simulation results are validated with two prototypes in gap-waveguide technology. The first one is a 180$^{o}$ phase shifter based on a glide-symmetric holey configuration that achieves a flat phase shift response over a wide frequency range (27.5\% frequency bandwidth). The second one is a filter based on a mirror-symmetric holey structure with 20-dB rejection from 63 GHz to 75 GHz.

physics.app-ph↗

arXiv2020

Reverse Janssen effect in narrow granular columns

When grains are added to a cylinder, the weight at the bottom is smaller than the total weight of the column, which is partially supported by the lateral walls through wall/grain frictional forces. This is known as the Janssen effect. Via a combined experimental and numerical investigation, here we demonstrate a reverse Jansen effect whereby the fraction of the weight supported by the base overcomes one. We characterize the dependence of this phenomenon on the various control parameters involved, rationalize the physical process responsible for the emergence of the compressional frictional forces responsible for the anomaly, and introduce a model to reproduce our findings. Contrary to prior assumptions, our results demonstrate that the constitutive relation on a material element can depend on the applied stress.

cond-mat.soft↗

arXiv2018

Thermodynamics and evolutionary biology through optimal control

We consider a particular instance of the lift of controlled systems recently proposed in the theory of irreversible thermodynamics and show that it leads to a variational principle for an optimal control in the sense of Pontryagin. Then we focus on two important applications: in thermodynamics and in evolutionary biology. In the thermodynamic context, we show that this principle provides a dynamical implementation of the Second Law, which stabilizes the equilibrium manifold of a system. In the evolutionary context, we discuss several interesting features: it provides a robust scheme for the coevolution of the population and its fitness landscape; it has a clear informational interpretation; it recovers Price equation naturally; and finally, it extends standard evolutionary dynamics to include phenomena such as the emergence of cooperation and the coexistence of qualitatively different phases of evolution, which we speculate can be associated with Darwinism and punctuated equilibria.

q-bio.PE↗

arXiv2016

Continuous Choreographies as Limiting Solutions of $N$-body Type Problems with Weak Interaction

We consider the limit $N\to +\infty$ of $N$-body type problems with weak interaction, equal masses and $-σ$-homogeneous potential, $0<σ<1$. We obtain the integro-differential equation that the motions must satisfy, with limit choreographic solutions corresponding to travelling waves of this equation. Such equation is the Euler-Lagrange equation of a corresponding limiting action functional. Our main result is that the circle is the absolute minimizer of the action functional among zero mean (travelling wave) loops of class $H^1$.

math.DS↗

arXiv2014

Complex groundwater flow systems as traveling agent models

Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits a complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective. Using a traveling agent model, we prove that this statistical behavior emerges when the medium is complex. Some heuristic reasoning is provided to justify both spatial and dynamic complexity, as the result of the superposition of an infinite number of stochastic processes. Even more, we show that this implies that non-Kolmogorovian probability is needed for its study, and provide a set of new partial differential equations for groundwater flow.

physics.flu-dyn↗

arXiv2013

A Selection Criterion for Patterns in Reaction-Diffusion Systems

Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided certain conditions are met. Turing's proposal has already been confirmed as a pattern formation mechanism in several chemical and biological systems and, due to their wide applicability, there is a great deal of interest in deciphering how to generate specific patterns under controlled conditions. However, techniques allowing one to predict what kind of spatial structure will emerge from Turing systems, as well as generalized reaction-diffusion systems, remain unknown. Here, we consider a generalized reaction diffusion system on a planar domain and provide an analytic criterion to determine whether spots or stripes will be formed. It is motivated by the existence of an associated energy function that allows bringing in the intuition provided by phase transitions phenomena. This criterion is proved rigorously in some situations, generalizing well known results for the scalar equation where the pattern selection process can be understood in terms of a potential. In more complex settings it is investigated numerically. Our criterion can be applied to efficiently design Biotechnology and Developmental Biology experiments, or simplify the analysis of hypothesized morphogenetic models.

q-bio.QM↗