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We study the mixed Dirichlet-Neumann problem for the Laplace equation in the complement of a bounded convex polygonal quadrilateral in the extended complex plane. The Dirichlet\,/\,Neumann conditions at opposite pairs of sides are $\{0,1\}$ and $\{0,0\},$ resp. The solution to this problem is a harmonic function in the unbounded complement of the polygon known as the \emph{potential function} of the quadrilateral. We compute the values of the potential function including its value at infinity., Comment: 14 pages, 5 figures

In this paper we discuss problems concerning the conformal condenser capacity of "hedgehogs", which are compact sets $E$ in the unit disk $\mathbb{D}=\{z:\,|z|<1\}$ consisting of a central body $E_0$ that is typically a smaller disk $\overline{\mathbb{D}}_r=\{z:\,|z|\le r\}$, $0

We determine the pressure of a cold and dense electron gas to a nearly complete next-to-next-to-next-to-leading order (N$^3$LO) in the fine-structure constant $\alpha_e$, utilizing a new result for the two-loop photon self-energy from a companion paper. Our result contains all infrared-sensitive contributions to the pressure at this order, including the coefficient of the $O(\alpha_e^3 \ln \alpha_e^{ })$ term, and leaves only a single coefficient associated with the contributions of unresummed hard momenta undetermined. Moreover, we explicitly demonstrate the complete cancellation of infrared divergences according to the effective field theory paradigm by determining part of the hard contributions at this order. Our calculation provides the first improvement to a 45-year-old milestone result and demonstrates the feasibility of the corresponding N$^3$LO calculation for cold and dense quark matter., Comment: 6 pages (main text), 6 pages (supplemental material) and 3 figures

We present the first complete calculation of the soft photon self-energy to the next-to-leading order in a hot and/or dense ultrarelativistic plasma in Quantum Electrodynamics (QED). The calculation is performed within the real-time formalism utilizing dimensional regularization in $4-2\epsilon$ dimensions, while the result is reported including explicit $O(\epsilon)$ terms in the zero-temperature limit. This information is required to extend the perturbative calculation of the pressure of cold and dense QED matter to partial next-to-next-to-next-to-leading order in a weak-coupling expansion, reported in a companion paper. These results pave the way for a similar future calculation in Quantum Chromodynamics., Comment: 46 pages, 11 figures

We explore the applicability of MATLAB for 3D computational fluid dynamics (CFD) of shear-driven indoor airflows. A new scale-resolving, large-eddy simulation (LES) solver titled DNSLABIB is proposed for MATLAB utilizing graphics processing units (GPUs). The solver is first validated against another CFD software (OpenFOAM). Next, we demonstrate the solver performance in three isothermal indoor ventilation configurations and the results are discussed in the context of airborne transmission of COVID-19. Ventilation in these cases is studied at both low (0.1 m/s) and high (1 m/s) airflow rates corresponding to $Re=5000$ and $Re=50000$. An analysis of the indoor CO$_2$ concentration is carried out as the room is emptied from stale, high CO$_2$ content air. We estimate the air changes per hour (ACH) values for three different room geometries and show that the numerical estimates from 3D CFD simulations may differ by 80-150 % ($Re=50000$) and 75-140 % ($Re=5000$) from the theoretical ACH value based on the perfect mixing assumption. Additionally, the analysis of the CO$_2$ probability distributions (PDFs) indicates a relatively non-uniform distribution of fresh air indoors. Finally, utilizing a time-dependent Wells-Riley analysis, an example is provided on the growth of the cumulative infection risk being reduced rapidly after the ventilation is started. The average infection risk is shown to reduce by a factor of 2 for lower ventilation rates (ACH=3.4-6.3) and 10 for the higher ventilation rates (ACH=37-64). The results indicate a high potential for DNSLABIB in various future developments on airflow prediction., Comment: 31 pages, 15 figures

Let $\Omega$ be the multiply connected domain in the extended complex plane $\overline{\C}$ obtained by removing $m$ non-overlapping rectilinear segments from the infinite strip $S=\{z\,:\, \left|\Im z\right|<\pi/2\}$. In this paper, we present an iterative method for numerical computation of a conformally equivalent bounded multiply connected domain $G$ in the interior of the unit disk $\D$ and the exterior of $m$ non-overlapping smooth Jordan curves. We demonstrate the utility of the proposed method through two applications. First, we estimate the capacity of condensers of the form $(S,E)$ where $E\subset S$ be a union of disjoint segments. Second, we determine the streamlines associated with uniform incompressible, inviscid and irrotational flow past disjoint segments in the strip $S$.

Zygmund dilations are a group of dilations lying in between the standard product theory and the one-parameter setting - in $\mathbb{R}^3 = \mathbb{R} \times \mathbb{R} \times \mathbb{R}$ they are the dilations $(x_1, x_2, x_3) \mapsto (\delta_1 x_1, \delta_2 x_2, \delta_1 \delta_2 x_3)$. The dyadic multiresolution analysis and the related dyadic-probabilistic methods have been very impactful in the modern product singular integral theory. However, the multiresolution analysis has not been understood in the Zygmund dilation setting or in other modified product space settings. In this paper we develop this missing dyadic multiresolution analysis of Zygmund type, and justify its usefulness by bounding, on weighted spaces, a general class of singular integrals that are invariant under Zygmund dilations. We provide novel examples of Zygmund $A_p$ weights and Zygmund kernels showcasing the optimality of our kernel assumptions for weighted estimates., Comment: v2: Added complementing details to the counterexamples in Section 2. 61 pages

We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions of certain three-dimensional kernels adapted to so-called Zygmund dilations, which is part of our motivation for studying these objects. We make the case that such kernels can, in many ways, be seen as part of the extended realm of standard kernels by proving that they satisfy both a T1 theorem and commutator estimates in a form reminiscent of the corresponding results for standard Calder\'on-Zygmund kernels. However, we show that one-parameter weighted estimates, in general, fail., Comment: 23 pages

We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by polycircular domains. Experimental error estimates are provided for the computed capacity and, when possible, the rate of convergence under refinement of discretisation is analysed. The main ingredients of the computation are two computational methods, on one hand the boundary integral equation method combined with the fast multipole method and on the other hand the $hp$-FEM method. The results obtained with these two methods agree with high accuracy.

We study the point pair function in subdomains $G$ of $\mathbb{R}^n$. We prove that, for every domain $G\subsetneq\mathbb{R}^n$, the this function is a quasi-metric with the constant less than or equal to $\sqrt{5}\slash2$. Moreover, we show that it is a metric in the domain $G=\mathbb{R}^n\setminus\{0\}$ with $n\geq1$. We also consider generalized versions of the point pair function, depending on an arbitrary constant $\alpha>0$, and show that in some domains these generalizations are metrics if and only if $\alpha\leq12$., Comment: 21 pages, 3 figures

In this review article, we describe the role of holography in deciphering the physics of dense QCD matter, relevant for the description of compact stars and their binary mergers. We review the strengths and limitations of the holographic duality in describing strongly interacting matter at large baryon density, walk the reader through the most important results derived using the holographic approach so far, and highlight a number of outstanding open problems in the field. Finally, we discuss how we foresee holography contributing to compact-star physics in the coming years., Comment: 86 pages, 19 figures; invited review article; v2: revised and published version

In this study, we introduce a novel open-source chemistry model for OpenFOAM to speed-up the reactive computational fluid dynamics (CFD) simulations using finite-rate chemistry. First, a dynamic load balancing model called DLBFoam is introduced to balance the chemistry load during runtime in parallel simulations. In addition, the solution of the cell-based chemistry problem is improved by utilizing an analytical Jacobian using an open-source library called pyJac and an efficient linear algebra library LAPACK. Combination of the aforementioned efforts yields a speed-up factor 200 for a high-fidelity large-eddy simulation spray combustion case compared to the standard OpenFOAM implementation. It is worth noting that the present implementation does not compromise the solution accuracy., Comment: Early work presented in European Combustion Meeting, Naples, 2021. For full paper please check arXiv:2105.12070

We study the interior and exterior moduli of polygonal quadrilaterals. The main result is a formula for a conformal mapping of the upper half plane onto the exterior of a convex polygonal quadrilateral. We prove this by a careful analysis of the Schwarz-Christoffel transformation and obtain the so-called accessory parameters and then the result in terms of the Lauricella hypergeometric function. This result enables us to understand the dissimilarities of the exterior and interior of a convex polygonal quadrilateral. We also give a Mathematica algorithm for the computation. In particular, we study the special case of an isosceles trapezoidal polygon $L$ and obtain some estimates for the coefficient of quasiconformal reflection over $L$ in terms of special functions and geometric parameters of~$L$., Comment: 30 pages, 4 figures

We discuss the problem of the reflection of light on spherical and quadric surface mirrors. In the case of spherical mirrors, this problem is known as the Alhazen problem. For the spherical mirror problem, we focus on the reflection property of an ellipse, and show that the catacaustic curve of the unit circle follows naturally from the equation obtained from the reflection property of an ellipse. Moreover, we provide an algebraic equation that solves Alhazen's problem for quadric surface mirrors., Comment: 19 pages, 5 figures

Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a non-linear equation of state that relates the surface tension to the surfactant concentration. For Newtonian turbulent bubbly flows, the effects of Triton X-100 and 1-Pentanol surfactant are examined. It is observed that the sorption kinetics highly affect the dynamics of bubbly flow. A minute amount of Triton X-100 is found to be sufficient to prevent the formation of bubble clusters restoring the single-phase behavior while even two orders of magnitude more 1-Pentanol surfactant is not adequate to prevent the formation of layers. For viscoelastic turbulent flows, it is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows, while the addition of small amount of surfactant (Triton X-100) in this system restores the polymer drag reduction resulting in $25\%$ drag reduction for the $Wi=4$ case.

The transport properties of dense QCD matter play a crucial role in the physics of neutron stars and their mergers, but are notoriously difficult to study with traditional quantum field theory tools. Specializing to the case of unpaired quark matter in beta equilibrium, we approach the problem through the machinery of holography, in particular the V-QCD and D3-D7 models, and derive results for the electrical and thermal conductivities and the shear and bulk viscosities. In addition we compare the bulk to shear viscosity ratio to the speed of sound and find that it violates the so-called Buchel bound. Our results differ dramatically from earlier predictions of perturbative QCD, the root causes and implications of which we analyze in detail., Comment: 31 pages + appendices, 6 figures

We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.