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Domain walls are a type of topological defects that can arise in the early universe after the spontaneous breaking of a discrete symmetry. They can form in several beyond the Standard Model theories with an extended Higgs sector such as the Next to-Two-Higgs-Doublet model (N2HDM). In this work, we discuss the domain wall solution related to the singlet scalar of the N2HDM and demonstrate the possibility of restoring the electroweak symmetry inside and in the vicinity of the domain wall. Such symmetry restoration can have profound implications on early universe cosmology as the weak sphaleron rate inside the domain wall would, in principle, be unsuppressed compared to the rate outside the wall. We also discuss the possibility of generating CP-violating vacua localized in the vicinity of the domain wall. Our work is a first step towards the realization of electroweak baryogenesis mediated by domain walls in the N2HDM., Comment: 44 pages, 26 figures, DESY-24-109

In several models of beyond Standard Model physics (BSM) discrete symmetries play an important role. For instance, in order to avoid flavor changing neutral currents (FCNC), a discrete $Z_2$ symmetry is imposed on Two-Higgs-Doublet-Models (2HDM). This can lead to the formation of domain walls (DW) as the $Z_2$ symmetry gets spontaneously broken during electroweak symmetry breaking (EWSB) in the early universe. Due to this simultaneous spontaneous breaking of both the discrete symmetry and the electroweak symmetry, the vacuum manifold has the structure of two disconnected 3-spheres and the formed domain walls can exhibit several special properties in contrast to standard domain walls. We focus on some of these properties such as CP and electric charge violating vacua localized inside the domain walls. The breaking of $U(1)_{em}$ inside the wall leads to the known phenomenon of "clash-of-symmetries" mechanism, meaning that the symmetry group inside the wall is smaller than the symmetry group far from the wall. We also discuss the scattering of top quarks off such types of domain walls and show, for example, that they can be reflected or transmitted off the wall as a bottom quark., Comment: 7 pages, 3 figures, Contribution to the proceedings of the European Physical Society Conference on High Energy Physics (EPS-HEP2023), 21-25 August 2023, Hamburg, Germany

Discrete symmetries play an important role in several extensions of the Standard Model (SM) of particle physics. For instance, in order to avoid flavor changing neutral currents, a discrete $Z_2$ symmetry is imposed on the Two-Higgs-Doublet Model (2HDM). This can lead to the formation of domain walls (DW) as the $Z_2$ symmetry gets spontaneously broken during electroweak symmetry breaking in the early universe and domain walls form between regions whose vacua are related by the discrete symmetry. Due to this simultaneous spontaneous breaking of both the discrete symmetry and the electroweak symmetry, the vacuum manifold consists of two disconnected 3-spheres. Such a non-trivial disconnected vacuum manifold leads to several choices for the vacua at two adjacent regions, in contrast to models where only the discrete symmetry gets spontaneously broken and the vacuum manifold consists of several disconnected points. Due to this, we end up with several classes of DW solutions having different properties localized inside the wall, such as charge and/or CP violating vacua. We discuss the properties of these different classes of DW solutions as well as the interaction of SM fermions with such topological defects leading to different exotic phenomena such as, for example, the top quark being transmitted or reflected off the wall as a bottom quark., Comment: 65 pages, 50 figures, 2 tables

In this study we investigate the heat load patterns in one building using multi-step forecasting model. We combine the Autoregressive models that use multiple eXogenous variables (ARX) with Seasonally adaptable Time of Week and Climate dependent models (S-TOW-C) (to correct model inaccuracies), to obtain a robust and accurate regression model that we called S-TOW-C-ARX used in time series forecasting. Based on the experiment results, it has been shown that the proposed model is suitable for short term heat load forecasting. The best forecasting performance is achieved in winter term where the prediction values are from 4 to 20 % away from the targets, which are commonly seen as very good values.

The dark matter abundance plays a crucial role in the determination of the valid parameter space of models both in the case of a discovery of dark matter and in the context of exclusion limits. Reliable theoretical predictions of the dark matter relic density require technically demanding precision calculations, which were so far limited in their automation due to challenges in the treatment of infrared divergences appearing in higher order calculations. In particular, massive initial states need to be considered in early Universe computations, so that the known dipole subtraction methods could not be directly exploited. We therefore provide a full generalization of the dipole subtraction method by Catani and Seymour to supersymmetric (SUSY) QCD with massive initial states. All dipole splitting functions and their integrated counterparts are given explicitly for four different dimensional schemes. To showcase their application, we apply our results to dark matter (co)annihilation processes in the context of the minimal supersymmetric Standard Model. We also demonstrate the accuracy of the dipole method by comparing our numerical results with those obtained with the phase space slicing method. Our analytical results will facilitate future automation of dark matter abundance calculations at next-to-leading order for both SUSY and non-SUSY models., Comment: 32 pages, 8 figures, 3 tables; updated to version published in Phys. Rev. D

Each grid block in a 3D geological model requires a rock type that represents all physical and chemical properties of that block. The properties that classify rock types are lithology, permeability, and capillary pressure. Scientists and engineers determined these properties using conventional laboratory measurements, which embedded destructive methods to the sample or altered some of its properties (i.e., wettability, permeability, and porosity) because the measurements process includes sample crushing, fluid flow, or fluid saturation. Lately, Digital Rock Physics (DRT) has emerged to quantify these properties from micro-Computerized Tomography (uCT) and Magnetic Resonance Imaging (MRI) images. However, the literature did not attempt rock typing in a wholly digital context. We propose performing Digital Rock Typing (DRT) by: (1) integrating the latest DRP advances in a novel process that honors digital rock properties determination, while; (2) digitalizing the latest rock typing approaches in carbonate, and (3) introducing a novel carbonate rock typing process that utilizes computer vision capabilities to provide more insight about the heterogeneous carbonate rock texture., Comment: 1-Acknowledgement section is updated. 2- References section is update with one additional reference

Although capillary and permeability are the two most important physical properties controlling fluid distribution and flow in nature, the interconnectivity function between them was a pressing challenge. Because knowing permeability leads to determining capillary pressure. Geodynamics (e.g., subsurface water, CO2 sequestration) and organs (e.g., plants, blood vessels) depend on capillary pressure and permeability. The first determines how far the fluid can reach, while the second determines how fast the fluid can flow in porous media. They are also vital to designing synthetic materials and micro-objects like membranes and micro-robotics. Here, we reveal the capillary and permeability intertwined behavior function. And demonstrate the unique physical connectors: pore throat size and network, linking capillary pressure and permeability. Our discovery quantifies the inverse relationship between capillary pressure and permeability for the first time, which we analytically derived and experimentally proved., Comment: 1- Added the Acknowledgement section

Permeability has a dominant influence on the flow properties of a natural fluid. Lattice Boltzmann simulator determines permeability from the nano and micropore network. The simulator holds millions of flow dynamics calculations with its accumulated errors and high consumption of computing power. To efficiently and consistently predict permeability, we propose a morphology decoder, a parallel and serial flow reconstruction of machine learning segmented heterogeneous Cretaceous texture from 3D micro computerized tomography and nuclear magnetic resonance images. For 3D vision, we introduce controllable-measurable-volume as new supervised segmentation, in which a unique set of voxel intensity corresponds to grain and pore throat sizes. The morphology decoder demarks and aggregates the morphologies boundaries in a novel way to produce permeability. Morphology decoder method consists of five novel processes, which describes in this paper, these novel processes are: (1) Geometrical 3D Permeability, (2) Machine Learning guided 3D Properties Recognition of Rock Morphology, (3) 3D Image Properties Integration Model for Permeability, (4) MRI Permeability Imager, and (5) Morphology Decoder (the process that integrates the other four novel processes)., Comment: 1- Added Affiliation section. 2- Added Remark section. 3- Applied grammar corrections

For defining the optimal machine learning algorithm, the decision was not easy for which we shall choose. To help future researchers, we describe in this paper the optimal among the best of the algorithms. We built a synthetic data set and performed the supervised machine learning runs for five different algorithms. For heterogeneous rock fabric, we identified Random Forest, among others, to be the appropriate algorithm., Comment: 1- Added Affiliation section. 2- Added Acknowledgement section

Automated image processing algorithms can improve the quality, efficiency, and consistency of classifying the morphology of heterogeneous carbonate rock and can deal with a massive amount of data and images seamlessly. Geoscientists face difficulties in setting the direction of the optimum method for determining petrophysical properties from rock images, Micro-Computed Tomography (uCT), or Magnetic Resonance Imaging (MRI). Most of the successful work is from the homogeneous rocks focusing on 2D images with less focus on 3D and requiring numerical simulation. Currently, image analysis methods converge to three approaches: image processing, artificial intelligence, and combined image processing with artificial intelligence. In this work, we propose two methods to determine the porosity from 3D uCT and MRI images: an image processing method with Image Resolution Optimized Gaussian Algorithm (IROGA); advanced image recognition method enabled by Machine Learning Difference of Gaussian Random Forest (MLDGRF). We have built reference 3D micro models and collected images for calibration of IROGA and MLDGRF methods. To evaluate the predictive capability of these calibrated approaches, we ran them on 3D uCT and MRI images of natural heterogeneous carbonate rock. We measured the porosity and lithology of the carbonate rock using three and two industry-standard ways, respectively, as reference values. Notably, IROGA and MLDGRF have produced porosity results with an accuracy of 96.2% and 97.1% on the training set and 91.7% and 94.4% on blind test validation, respectively, in comparison with the three experimental measurements. We measured limestone and pyrite reference values using two methods, X-ray powder diffraction, and grain density measurements. MLDGRF has produced lithology (limestone and Pyrite) volumes with 97.7% accuracy., Comment: 1- Added Affiliation section. 2- Updated the Acknowledgement section

In this paper, we examine linear programming (LP) relaxations based on Bernstein polynomials for polynomial optimization problems (POPs). We present a progression of increasingly more precise LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. The well-known bounds on Bernstein polynomials over the unit box combined with linear inter-relationships between Bernstein polynomials help us formulate "Bernstein inequalities" which yield tighter lower bounds for POPs in bounded rectangular domains. The results can be easily extended to optimization over polyhedral and semi-algebraic domains. We also examine techniques to increase the precision of these relaxations by considering higher degree relaxations, and a branch-and-cut scheme

In this paper, we deal with the problem of synthesizing static output feedback controllers for stabilizing polynomial systems. Our approach jointly synthesizes a Lyapunov function and a static output feedback controller that stabilizes the system over a given subset of the state-space. Specifically, our approach is simultaneously targeted towards two goals: (a) asymptotic Lyapunov stability of the system, and (b) invariance of a box containing the equilibrium. Our approach uses Bernstein polynomials to build a linear relaxation of polynomial optimization problems, and the use of a so-called "policy iteration" approach to deal with bilinear optimization problems. Our approach can be naturally extended to synthesizing hybrid feedback control laws through a combination of state-space decomposition and Bernstein polynomials. We demonstrate the effectiveness of our approach on a series of numerical benchmark examples.

In this paper, we examine linear programming (LP) based relaxations for synthesizing polynomial Lyapunov functions to prove the stability of polynomial ODEs. A common approach to Lyapunov function synthesis starts from a desired parametric polynomial form of the polynomial Lyapunov function. Subsequently, we encode the positive-definiteness of the function, and the negative-definiteness of its derivative over the domain of interest. Therefore, the key primitives for this encoding include: (a) proving that a given polynomial is positive definite over a domain of interest, and (b) encoding the positive definiteness of a given parametric polynomial, as a constraint on the unknown parameters. We first examine two classes of relaxations for proving polynomial positivity: relaxations by sum-of-squares (SOS) programs, against relaxations that produce linear programs. We compare both types of relaxations by examining the class of polynomials that can be shown to be positive in each case. Next, we present a progression of increasingly more powerful LP relaxations based on expressing the given polynomial in its Bernstein form, as a linear combination of Bernstein polynomials. The well-known bounds on Bernstein polynomials over the unit box help us formulate increasingly precise LP relaxations that help us establish the positive definiteness of a polynomial over a bounded domain. Subsequently, we show how these LP relaxations can be used to search for Lyapunov functions for polynomial ODEs by formulating LP instances. We compare our approaches to synthesizing Lyapunov functions with approaches based on SOS programming relaxations.