Homogeneous Geometry Research Articles

Semi-symmetric metric gravity: From the Friedmann–Schouten geometry with torsion to dynamical dark energy models

In this paper, we develop a geometric generalization of General Relativity based on the semi-symmetric metric connection introduced by Friedmann and Schouten in 1924. Although the mathematical properties of this connection, which allows for torsion, have been extensively studied, its physical implications remain underexplored. We provide a detailed exposition of the differential geometric aspects of semi-symmetric connections and formulate the corresponding field equations induced by the specific form of torsion we are investigating. We consider the cosmological applications of the theory by deriving the generalized Friedmann equations in a flat, homogeneous and isotropic geometry. The Friedmann equations also include some supplementary terms as compared to their general relativistic counterparts, which can be interpreted as a geometric type dark energy. To evaluate the proposed theory, we consider three cosmological models — the first with constant effective density and pressure, the second with the dark energy satisfying a linear equation of state, and a third one with a polytropic equation of state. We also compare the predictions of the semi-symmetric metric gravitational theory with the observational data for the Hubble function, and with the predictions of the ΛCDM model. Our findings indicate that the semi-symmetric metric cosmological models give a good description of the observational data, and for certain values of the model parameters, they can reproduce almost exactly the predictions of the ΛCDM paradigm. Consequently, Friedmann’s initially proposed geometry emerges as a credible alternative to standard general relativity, in which dark energy has a purely geometric origin.

Significance of a quadratically varying deceleration parameter in scalar field-dominated model and cosmic acceleration

In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein’s field equations, achieved through a parametrization of the deceleration parameter [Formula: see text] in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe’s evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe.

Influence of sedimentary structure and pore-size distribution on upscaling permeability and flow enhancement due to liquid boundary slip: A pore-scale computational study

Low-permeability sedimentary formations, such as tight sandstones, exhibit fluid flow and transport phenomena distinct from those in conventional porous systems due to the dominance of micro- to nanometer-sized pores and variable amounts of boundary slip. The widely used traditional no-slip boundary condition often fails to accurately describe fluid behavior in these formations. A knowledge gap exists in understanding how liquid slip influences fluid dynamics in complex, heterogeneous sedimentary structures, as previous studies have primarily focused on simplified, homogeneous pore geometries. In this study, we investigated the impact of boundary slip on low-Reynolds number fluid dynamics within synthetically designed two-dimensional graded and random pore networks with varying pore-size distributions to account for heterogeneity. Our results showed that velocity variance increased with increasing heterogeneity, following a power-law relationship. The power-law exponents decreased with boundary slip, quantifying how boundary slip mitigated the impact of heterogeneity on velocity variance. We developed a theoretical model to predict asymptotic flow enhancement and derived constitutive relations to estimate the coefficient C and maximum flow enhancement (ΔE) based on the pore-to-grain size ratio and porosity. Energy dissipation increased with both heterogeneity and boundary slip, which we identified as the primary mechanism contributing to asymptotic flow enhancement. This relationship was illustrated by a 1:1 linear correlation between maximum energy dissipation and maximum flow enhancement, regardless of heterogeneity, indicating that energy dissipation due to boundary slip entirely controls the emerging fluid dynamics. The presented theoretical model and constitutive equations offer practical applications for optimizing fluid dynamics in heterogeneous formations.

Cosmological implications of the Weyl geometric gravity theory

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. We use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

Gauge-invariant cosmological perturbations in general teleparallel gravity

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum–hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the f(G), f(T) and f(Q) class of theories.

Twisted domains in ferroelectric nematic liquid crystals

Ferroelectric nematics present properties promising for applications, which strongly depend on the confinement conditions and the presence of defects. In this work, we have observed and analysed textures in the cells with homogeneous geometry for a ferroelectric nematogen. The studied compound designated NF6 reveals the ferroelectric nematic phase, NF, directly on cooling from the isotropic phase. The NF phase is stable and persists down to the room temperatures. Textures in the homogeneous cell with antiparallel alignment prefer to be arranged in twisted domains with borderlines oriented preferentially in the perpendicular direction with respect to the surface alignment (rubbing direction). We have described these domains and developed a model of 2π disclinations, which are separating the areas with an opposite twist sense. We discuss the character of disclination charge and explained why these disclination lines prefer to be oriented perpendicularly to the rubbing direction.

Thermal performance of clay bricks with different fillings: a CFD analysis

The thermal conductivity of 15 loadbearing and infill bricks was calculated through a Computational Fluid Dynamic (CFD) analysis. Clay bricks filled with air, expanded polystyrene EPS, and graphitized expanded polystyrene were selected from the catalogue of the manufacturer F.B.M. - Fornaci Briziarelli Marsciano. The company provided the geometric features of each block and the thermal characteristics of the clay mix and the filling. The thermal conductivity value of each air cavity was calculated in compliance with UNI EN ISO 6946. Each volume was discretized in triangular meshes. The equivalent thermal conductivity of each block was calculated starting from the simulation of the isotherms trend inside the sample and from the heat flux passing through it. The obtained results were discussed depending on the filling, the geometry, and the hole percentage. In general, thermal conductivity increases with hole percentage in the bricks with air. Similar geometries have similar thermal behaviour. EPS or graphitized EPS involve better thermal performance as the hole percentage increases. Finally, the influence of the different orientations of the blocks was investigated. Equivalent thermal conductivity values increase for horizontally-brick placed, especially in homogeneous and compact geometries.

Utilization of Prunus serrulata leaf extract for the synthesis and characterization of ZnO nanoparticles

Using a green route for the synthesis of nanoparticles has become popular in recent years due to its easier, eco-friendly, faster and cheaper nature. This study explores the synthesis of ZnO nanoparticles utilizing, for the first time, Prunus serrulata (Japanese Cherry Blossom) leaf extract as both a reducing and capping agent. The characterization of the nanoparticles was performed by employing several instrumental techniques. The X-Ray Diffraction (XRD) method was utilized to identify the amorphous crystal structure of the ZnO nanoparticles. Scanning Electron Microscopy (SEM) and Scanning Transmission Electron Microscopy (STEM) were used to determine the homogenous and spherical geometry, having a size of 5–10 nm. X-Ray Photoelectron Spectroscopy (XPS) was used to observe the surface of the nanoparticles, which were present in the metal oxide form. Fourier Transform-Infrared spectroscopy (FT-IR) was also utilized to understand which types of organic groups are responsible for the stabilization of the nanoparticles.

Sensitivity and specificity of secondary dose calculation for head and neck treatment plans.

Secondary dose calculation (SDC) with an independent algorithm is one option to perform plan-specific quality assurance (QA). While measurement-based QA can potentially detect errors in plan delivery, the dose values are typically only compared to calculations on homogeneous phantom geometries instead of patient CT data. We analyzed the sensitivity and specificity of an SDC software by purposely introducing different errors and determined thresholds for optimal decisions. Thirty head and neck VMAT plans and 30 modifications of those plans, including errors related to density and beam modelling, were recalculated using RadCalc with a Monte Carlo algorithm. Decision thresholds were obtained by receiver operating characteristics (ROC) analysis. For comparison, measurement-based QA using the ArcCHECK phantom was carried out and evaluated in the same way. Despite optimized decision thresholds, none of the systems was able to reliably detect all errors. ArcCHECK analysis using a 2%/2mm criterion with a threshold of 91.1% had an area under the curve (AUC) of 0.80. Evaluating differences in recalculated and planned DVH parameter of the target structures in RadCalc with a 2% threshold an AUC of 0.86 was achieved. Out-of-field deviations could be attributed to weaknesses in the beam model. Secondary dose calculation with RadCalc is an alternative to established measurement-based phantom QA. Different tools catch different errors; therefore, a combination of approaches should be preferred.

Mesoporous Composite Bioactive Compound Delivery System for Wound-Healing Processes.

Currently, the treatment of wounds is still a challenge for healthcare professionals due to high complication incidences and social impacts, and the development of biocompatible and efficient medicines remains a goal. In this regard, mesoporous materials loaded with bioactive compounds from natural extracts have a high potential for wound treatment due to their nontoxicity, high loading capacity and slow drug release. MCM-41-type mesoporous material was synthesized by using sodium trisilicate as a silica source at room temperature and normal pressure. The synthesized mesoporous silica was characterized by using Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), N2 absorption-desorption (BET), Dynamic Light Scattering (DLS) and Fourier transform infrared spectroscopy (FT-IR), revealing a high surface area (BET, 1244 m2/g); pore diameter of approx. 2 nm; and a homogenous, ordered and hexagonal geometry (TEM images). Qualitative monitoring of the desorption degree of the Salvia officinalis (SO) extract, rich in ursolic acid and oleanolic acid, and Calendula officinalis (CO) extract, rich in polyphenols and flavones, was performed via the continuous recording of the UV-VIS spectra at predetermined intervals. The active ingredients in the new composite MCM-41/sage and marigold (MCM-41/SO&CO) were quantified by using HPLC-DAD and LC-MS-MS techniques. The evaluation of the biological composites' activity on the wound site was performed on two cell lines, HS27 and HaCaT, naturally involved in tissue-regeneration processes. The experimental results revealed the ability to stimulate collagen biosynthesis, the enzymatic activity of the main metalloproteinases (MMP-2 and MMP-9) involved in tissue remodeling processes and the migration rate in the wound site, thus providing insights into the re-epithelializing properties of mesoporous composites.

Homogeneous and anisotropic cosmologies with affine EoS: a dynamical system perspective

We study a class of homogeneous and anisotropic geometries with affine equation of state (EoS) for different physically plausible scenarios of the universe evolution using dynamical system technique. We analyze the locally rotationally symmetric Bianchi I (LRS BI), Bianchi III (LRS BIII) and Bianchi V (LRS BV) geometry for the exhibition of the effects of affine EoS in the model. The model exhibits stable attractor which is also isotropic and thus, it may explain the late-time accelerated expansion of the universe. The model also possess stiff matter-, radiation- and matter-dominated phases prior to the dark energy assisted accelerating phase which are confirmed by the behaviours of effective equation of state and deceleration parameters. We use the statefinder diagnostic which is a geometrical diagnostic to explore model independent features of the cosmological dynamical system. The LRS BI, BIII and BV geometry based dynamical systems exhibit r=1,s=0(Lambda cold dark matter model) at late-times, which is compatible with the observations. The dynamical system for the Kantowski–Sachs model yields synchronous bounce on the basis of the model parameters. It also yields a late-time attractor which may explain the accelerated expansion of the universe in the model. The qualitative differences between LRS BIII and BV cosmological dynamical systems have also been discussed.

First BGG operators via homogeneous examples

We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many interesting properties and interpretations.

Spatial-temporal tracking of molecular species in Geant4-DNA track structure simulations

Monte Carlo particle transport codes have been used to simulate the radiolysis of water and subsequent evolution of molecular species during the chemical stage. In Geant4, accounting of molecules is performed using a molecule counter which provides only a global molecule count. We developed a modular counter implementation that was used to perform spatial-temporal tracking of molecule counts. This custom counter was validated in homogeneous and simplistic split geometries for 1 MeV electrons and 50 MeV protons.Using a spherical cell with one nucleus and one hundred mitochondria as an example, the radiolytic yields in the cytoplasm, nucleus, and mitochondria were compared between targeted (electrons originating from within mitochondria) and unspecific (electrons originating from within cytoplasm) for (very) low energy electrons with kinetic energies of 100 eV to 1 keV.At short times radiolytic yields in source volumes were consistent with reference yields obtained in a large homogeneous volume. Past 1 ns diffusion out of the source volumes led to yield reductions. For volumes abutting the source volumes radiolytic yields at short times strongly depended on track end effects, most pronounced for 100 eV electrons. Similarly, diffusion out of the source volumes greatly increased yields in abutting volumes past 1 ns with magnitude decreasing and time of increase increasing with increasing electron energy. For higher energy electron beams (100 keV and 200 keV) radiolytic yields in all volumes were consistent with reference yields for large statistics.Thus, in cases where energy deposit sites are uniformly distributed in the volume of interest and energies of the charged particles are high to avoid track end effects reference yields may be used in place of resource intensive chemical stage simulations. Spatially heterogeneous energy deposits, as observed in targeted ɑ or β radiation therapy or with targeted nanoparticles, using a spatially sensitive molecule counter is suggested when estimating radiolytic yields outside of the source volumes or at distances that are within the diffusion range of the molecules of interest.

The “LED‐version” of the electron gun

SummaryWe report on our progress to develop and optimize electron sources for practical applications. A simple fabrication process is introduced based on a wafer dicing saw and a wet chemical etch step without the need for a clean room. Due to the formation of crystal facets the samples show a homogeneous geometry throughout the array. Characterization techniques are developed to systematically compare various arrays. A very defined measurement procedure based on current controlled IV‐sweeps as well as lifetime measurements at various currents is proposed. To investigate the current distribution in the array a commercial CMOS detector is used and shows the potential for in depth analysis of the arrays. Finally, a compact hermetically sealed housing is presented enabling electron generation in atmospheric pressure environments.

Effect of piston bowl geometry and spray angle on engine performance and emissions in HCCI engine using multi‐stage injection strategy

AbstractThe homogeneous charge compression ignition (HCCI) and combustion chamber geometry play significant roles in improving the potential of compression ignition engines and their environmental sustainability. However, a major hindrance to the progress of HCCI technology has been the notable decline in brake thermal efficiency and emit high levels of hydrocarbon (HC) and carbon monoxide (CO) which is mainly due to the low temperatures during combustion and low post oxidation of these components. Combustion chambers like hemispherical combustion chamber (TCC) and toroidal combustion chamber (TCC) are known to provide better combustion characteristics due to their increased surface‐to‐volume ratio. Moreover, injection timing and spray position have shown a significant effect on the controlling onset of combustion and emission in HCCI engine. Therefore, the primary objective of this numerical study is to enhance the engine characteristics in HCCI mode using an HCC and TCC piston bowl geometry coupled with multistage injection and compare the results with flat piston bowl geometry. The results show that the toroidal shape piston geometry provides 3%–5% higher brake thermal efficiency compared to the conventional piston geometry. Additionally, the energy balance analysis revealed that the combination of modified piston geometry and multi stage injection improved the combustion process by reducing the energy losses due to incomplete combustion and heat transfer to the engine walls. These findings suggest that the proposed injection strategy combined with modified piston geometry has the potential to enhance the performance of HCCI engines and reduce their environmental impact.

Accelerating cosmology from Λ < 0 gravitational effective field theory

A large class of Λ < 0 cosmologies have big-bang/big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.

Selective Area Epitaxy of GaN Nanostructures: MBE Growth and Morphological Analysis

This work presents the selective area epitaxy of GaN nanostructures grown on Ga-polar GaN/sapphire substrates by plasma-assisted molecular beam epitaxy. We demonstrate three types of nanostructures, including nanowires, nanofins, and nanorings on GaN-on-sapphire templates as well as investigate the ways of controlling their morphology, and orientation of sidewall plus top facets. A range of growth conditions including low to high Ga flux were employed during selective area epitaxy to develop these nanostructures with homogenous geometry and near vertical and smooth sidewalls. Using appropriate growth conditions and mask patterning orientations, nonpolar nanofin grids containing both/either m-/a-planes with as low as 260 nm fin width and up to six interconnects are demonstrated with smooth sidewalls. Based on these experimental results, we developed a growth model that takes different sidewall facets and orientations into account. The model generalizes the experimental results well and explains the growth conditions for the nanostructures. This study serves to advance the understanding of selective area epitaxy for defining complex III-nitride nanostructures that constitute an active area of research and development in the fields of nanotechnology and nanoscience.

Electrokinetic ion rectification in the coupling asymmetric charged nanochannel

Ion transport in nanochannels attracts increasing attention with the advance of nanotechnology, where ion rectification has been intensively studied due to its diode-like electrokinetic behavior. However, the electrochemical interface in most ion rectification is not uniform but involves asymmetric-charged characteristics that offer new degrees of electrical double layer (EDL) confinement. Herein, we investigate the ion transport in coupling asymmetric charged nanochannel to evaluate how the asymmetric geometry and surface charge influences the ion rectification performance. The results show that at low surface charge gradient, the coupling effect enhances ion rectification performance. While at high surface charge gradient, an anomalous electrokinetic behavior is observed that coupling effect deteriorates ion rectification performance. Further analysis discloses that the enhancement-deterioration transition threshold depends on the coordination mechanism of asymmetric geometry and surface charge. It is found that the asymmetric geometry shaped nanochannel with low surface charge gradient and homogeneous geometry shaped nanochannel with high surface charge gradient have the better ion rectification performance. This work fills the gap in understanding the coupling asymmetry effect on ion rectification, providing the useful guidance to design nanofluidic energy devices.

Homogeneous and isotropic cosmology in general teleparallel gravity

We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can further be restricted to the torsion-free and metric-compatible cases. We apply our results to several classes of general teleparallel gravity theories and derive their cosmological dynamics for all five branches. Our results show that for large subclasses of these theories the dynamics reduce to that of closely related metric or symmetric teleparallel gravity theories, while for other subclasses up to two new scalar degrees of freedom participate in the cosmological dynamics.