Computation of conformal invariants

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies to a wide variety of geometries: domains are assumed to have smooth or piecewise smooth boundaries. The method we use is based on the boundary integral equation method developed and implemented in [1]. A characteristic feature of this method is that, with small changes in the code, a wide spectrum of problems can be treated. We compare the performance and accuracy to previous results in the cases when numerical data is available and also in the case of several model problems where exact results are available. (C) 2020 Elsevier Inc. All rights reserved

Isoperimetric properties of condenser capacity

For compact subsets E of the unit disk D we study the capacity of the condenser (D, E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic triangle and arrive at the conjecture that of all triangles with the same hyperbolic area, the equilateral triangle has the least capacity.

Isoperimetric properties of condenser capacity

For compact subsets E of the unit disk D we study the capacity of the condenser (D,E) by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic triangle and arrive at the conjecture that of all triangles with the same hyperbolic area, the equilateral triangle has the least capacity

Numerical computation of the capacity of generalized condensers

We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the generalized condenser are bordered by piecewise smooth Jordan curves or are rectilinear slits. The presented method is used also to compute the harmonic measure in multiply connected domains

Analytical Treatment of the Oscillating Yukawa Potential

Using a suitable Laguerre basis set that ensures a tridiagonal matrix representation of the reference Hamiltonian, we were able to evaluate in closed form the matrix elements of the generalized Yukawa potential with complex screening parameter. This enabled us to treat analytically both the cosine and sine-like Yukawa potentials on equal footing and compute their bound states spectrum as the eigenvalues of the associated analytical matrix representing their Hamiltonians. Finally we used a carefully designed complex scaling method to evaluate the resonance energies and compared our results satisfactorily with those obtained in the literature.Comment: 8 pages 2 table

“Top Trends and Challenges of Digital Technologies to enhance the Efficiency of Building Thermal Insulation and the Reality of its Application in Riyadh, Saudi Arabia”

تشكل التقنيات الرقمية إحدى أهم مظاهر التقدم الحضاري في القرن الحادي والعشرين والتي اثرت بشكل كبير علـى النتاج المعماري تصميماً وانشاءً سواء على مستوى تقنيات المواد، أو تقنيات التطبيقات الرقمية أو تقنيات الأجهزة الإلكترونية الرقمية التي تساعد في تحسين أداء المباني عموماً ورفع كفاءة أداء العزل الحراري على وجه الخصوص. وعلى الرغم من انتشار تطبيق تقنيات مواد البناء في العديد من المجالات التي ترتبط بالعزل الحراري الى جانب تطبيقها وقياس ادائها باستخدام بالتقنيات الرقمية في أغلب الدول المتقدمة، الا انها لم تصل الى المستوى المأمول في السوق المحلي بالمملكة وهو ما يمثل إشكالية البحث الرئيسية. ويهدف البحث إلى استكشاف أهم اتجاهات وتحديات التقنيات الرقمية التي تساهم في رفع كفاءة العزل الحراري للمباني، ودعــم ذلك بعــرض عـدد مـن الحالات الدراسـية التـي توضـح وتؤكـد مــا تــم التوصــل إليــه، ورصد واقع تطبيقها في مدينة الرياض. واعتمد البحث في معالجة المشكلة البحثية على المنهج الوصفي التحليلي على مرحلتين: تعتمد الأولى على المراجعات الأدبية لاستكشاف اهم اتجاهات وتحديات التقنيات الرقمية التي تساهم في رفع كفاءة العزل الحراري للمباني، بينما تعتمد الثانية على رصد واقع تطبيق هذه التقنيات بالسوق المحلي في المملكة العربية السعودية. وخلص البحث إلى تحديد الأهمية النسبية لما تم استكشافه من اتجاهات وتحديات، وإلى أن تطبيق هذه الاتجاهات مازال في بدايته ويجب دعمه من خلال زيادة الوعي والمعرفة لدى المعماريين والمتخصصين في أهمية استخدام التقنيات الرقمية ووضع النظم والاشتراطات الكفيلة بزيادة تطبيق التقنيات الرقمية في المكاتب الهندسية من الجهات الحكومية ذات العلاقة بالعزل الحراري. ومن اهم ما يؤكد أهمية هذا البحث هو توافق أهدافه مع رؤية المملكة 2030 والتي تضمنت توجهات المملكة للتحول الرقمي وتحقيق الاستدامة وتخفيض استهلاك الطاقة

Singular Short Range Potentials in the J-Matrix Approach

We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1/r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.Comment: 14 pages, 5 tables, 2 figure

Hydrocracking of Waste Cooking Oil as Renewable Fuel on NiW/SiO2-Al2O3 Catalyst

Considering the plant-derived oil as a renewable source for production of alternative fuel, the waste cooking oil (WCO) was directly converted in this work as an alternative fuel by using the commercially available NiW/SiO2-Al2O3 hydrocracking catalyst. This conversion was performed in a fixed bed flow reactor at varying operating conditions of temperature (375-450°C), pressure (2, 6 MPa), and LHSV (1, 2, 4h-1). The H2/WCO ratio was kept constant at 400 V/V. The distribution of fuel fractions was evaluated via ASTM distillation. The GC was used for analysis of individual hydrocarbon products. The FTIR was used to investigate the progress of oil conversion. The results showed that the catalytic hydrocracking of WCO generates fuels that have chemical and physical properties comparable to those specified for petroleum-based fuels. The amount of kerosene/diesel fractional product decreased with increasing the temperature and pressure and decreasing the LHSV; while gasoline fuel increased. The reaction was found to follow the second order mechanism, where the estimated activation energy Ea was 56 kj mol-1

Biological-Based Produced Water Treatment Using Microalgae: Challenges and Efficiency

Produced water (PW) is the most significant waste stream generated in the oil and gas industries. The generated PW has the potential to be a useful water source rather than waste. While a variety of technologies can be used for the treatment of PW for reuse, biological-based technologies are an effective and sustainable remediation method. Specifically, microalgae, which are a costeffective and sustainable process that use nutrients to eliminate organic pollutants from PW during the bioremediation process. In these treatment processes, microalgae grow in PW free of charge, eliminate pollutants, and generate clean water that can be recycled and reused. This helps to reduce CO2 levels in the atmosphere while simultaneously producing biofuels, other useful chemicals, and added-value products. As such, this review focuses on PW generation in the oil and gas industry, PW characteristics, and examines the available technologies that can be used for PW remediation, with specific attention to algal-based technologies. In addition, the various aspects of algae growth and cultivation in PW, the effect of growth conditions, water quality parameters, and the corresponding treatment performance are presented. Lastly, this review emphasizes the bioremediation of PW using algae and highlights how to harvest algae that can be processed to generate biofuels for added-value products as a sustainable approach.Scopu