Double Box Research Articles

Motivic Geometry of two-Loop Feynman Integrals

Abstract We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into mixed Tate pieces and the Hodge structures of families of hyperelliptic, elliptic or rational curves depending on the space-time dimension. For two-loop graphs with a small number of edges, we give more precise results. In particular, we recover a result of Bloch (Double box motive. SIGMA 2021;17,048) that in the well-known double-box example, there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the non-planar two-loop tardigrade graph is that of a K3 surface. In an appendix by Eric Pichon-Pharabod, we argue via high-precision numerical computations that the Picard number of this K3 surface is generically 11 and we compute the expected lattice polarization. Lastly, we show that generic members of the ice cream cone family of graph hypersurfaces correspond to the pairs of sunset Calabi–Yau varieties.

Comprehensive Study on Design and Construction Methodology of Precast Box-Type Minor Bridge

Abstract: Bridges are crucial elements in modern transportation infrastructure, facilitating connectivity across different points on roads. In areas with challenging topography and site conditions, such as rivers or streams, it becomes essential to construct structures that allow for the unobstructed flow of water. These structures, commonly known as bridges and culverts, are vital for maintaining natural water flow. The flow rate through these water bodies is a key consideration in the design of bridges, culverts, and other drainage structures. This study focuses on the design of precast box type minor bridge, exploring alternative design modules that incorporate fixed and hinged end condition for both top and bottom slabs of single and double box cells. The objective is to determine the optimal design configuration for box Type Minor Bridge components, balancing considerations of functionality, efficiency, and cost-effectiveness.

Near mass-shell double boxes

Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle virtualities. The latter serve as regulators of infrared divergences, thus making these observables finite in four space-time dimensions. In this paper, we use the method of canonical differential equations for the calculation of (non)planar double box integrals in the near mass-shell kinematical regime, i.e., where virtualities of external particles are much smaller than the Mandelstam variables involved. We deduce a basis of master integrals with uniform transcendental weight based on the analysis of leading singularities employing the Baikov representation as well as an array of complementary techniques. We dub the former asymptotically canonical since it is valid in the near mass-shell limit of interest. We iteratively solve resulting differential equations up to weight four in terms of multiple polylogarithms.

AI and the transformation of industrial work: Hybrid intelligence vs double-black box effect

It is uncertain how the application of artificial intelligence (AI) technology transforms industrial work. We address this question from the perspective of cognitive systems, which, in this case, includes considerations of AI and process transparency, resilience, division of labor, and worker skills. We draw from a case study on glass tempering that includes a machine-vision-based quality control system and an advanced automation process control system. Based on task analysis and background literature, we develop the concept of hybrid intelligence that implies balanced AI transparency that supports upskilling and resilience. So-called fragmented intelligence, in turn, may result from the combination of the complexity of advanced automation along with the complexity of the process physics that places critical emphasis on expert knowledge. This combination can result in the so-called “double black box effect”, given that designing for understandability for the line workers might not be feasible: expert networks are needed for resilience.

Examining the influence of magnetic field on a donor dopant’s photoionization cross-section in a double quantum box

This study systematically explored the binding energy and the photoionization cross-section (PCS) of a hydrogenic shallow donor impurity within a GaAs double quantum box structure incorporated into a Ga(1−x)Alx As matrix under the influence of an external intense magnetic field. The computations are performed using the effective-mass approximation (EMA) and the finite element method (FEM), taking into account a finite potential across all surfaces of the nanosystem. The results emphasize the significant role of the magnetic field, primarily in enhancing the donor binding energy within the double quantum box system. We demonstrate that increasing the magnetic field results in an augmentation of binding energy across various aluminum concentrations. The PCS of a shallow donor impurity undergoes a blue shift when shifted from the barrier center to the box center, attributed to the increased binding energy. When the double quantum box is subjected to a magnetic field effect, the amplitude peaks of PCS show an elevation coupled with a blue shift. By setting magnetic field values at 0 T, 35 T, or 70 T and varying aluminum concentrations, we observe a shift in the PCS towards higher energy levels along with an increase in peak amplitude. We also study the PCS of the donor impurity as a function of photon energy, mainly examining the effects of box width and barrier width modifications in the double quantum box.

Flow around single and two tandem rectangular cylinders with various single-side fairings

The shape of single-side wind fairing, which is the longitudinal triangular prism that tailors the outer side of a bridge deck, is key to the aerodynamic performances of double streamlined box girders used in long-span bridges. Uniform flow past single and double 4:1 rectangular cylinders with various single-side fairings are investigated using large-eddy simulation at a Reynolds number of 1.1 × 104. Various fairing nose angles and heights are compared. The wind loading and flow characteristics of the cylinders are discussed. The upstream fairing shows a larger reduction of mean drag and fluctuating lift on double cylinders than on a single cylinder. The fairing nose angle has a stronger influence on the wind loading than the nose height. By adding the fairing, sharpening the fairing nose, or lifting the fairing nose, the lateral recirculation zones are shortened while the rear recirculation zone barely changes, leading to different influences on the surface pressure. The upstream fairing is effective in reducing the vertical range and complexity of vortex structures around single and double cylinders.

Deep Neural Network-Based Cloth Collision Detection Algorithm

The quality of collision detection algorithm directly affects the performance of the whole simulation system. To address the low efficiency and low accuracy in detecting the collisions of flexible cloths in virtual environments, this paper proposes an oriented bounding box (OBB) algorithm with a simplified model, tree structure for a root-node double bounding box, and continuous collision detection algorithm incorporating an OpenNN-based neural network optimization. First, for objects interacting with the cloths with more complex modeling, the model is simplified with a surface simplification algorithm based on the quadric error metrics, and the simplified model is used to construct an OBB. Second, a bounding box technique commonly used for collision detection is improved, and a root-node double bounding box algorithm is proposed to reduce the construction time for the bounding box. Finally, neural networks are used to optimize the continuous collision detection algorithm, as neural networks can efficiently process large amounts of data and remove disjoint collision pairs. An experiment shows that the construction of an OBB using the simplified model is almost identical to that of the original model, but the taken to construct the OBB is reduced by a factor of approximately 2.7. For the same cloth, it takes 5.51%–11.32% less time to run the root-node double bounding box algorithm than the traditional-hybrid bounding box algorithm. With an average removal rate nearly identical to that of the traditional filtering method, the elapsed time is reduced by 7%–11% by using the continuous collision detection algorithm based on an OpenNN neural network optimization. The simulation results are realistic and in line with the requirements for real-time cloth simulations.

Microstructure and mechanical properties of T2 copper /316L stainless steel explosive welding composite with small size wavy interface

Copper/stainless steel composite is often used for preparation of superconducting busbar “double box” lap joints. However, it is a challenge for the large thickness T2 copper/316L stainless steel composite is fabricated by explosive welding, because of the bonding interface is always present many problems such as large ripple size, many microscopic defects, low bonding strength and poor sealing etc. In this paper, the big-thickness T2 copper/316L stainless steel composite with small size wavy interface was successfully fabricated by explosive welding. Microstructure of bonding interface indicated that the welding process could be divided into three stages: detonation growth stage, detonation stabilization stage, detonation descent stage. The morphology of bonding interface presented a regular wavy interface and no defects such as cracks, voids and intermetallic compound were formed in the stable stage, which was consistent with the results of ultrasonic and permeability quality inspection. The hardness of copper side and stainless steel side close to the bonding interface reached 131HV and 432HV, respectively. Dynamic recrystallization and fine grain generated in the bonding interface. The mechanical properties of tensile strength, pull-off strength and shear strength in the stable detonation stage is greater than 110 MPa, which is meeting the requirements of preparation of superconducting busbar “double box” lap joints. The deformation failure mainly occurred in the copper side near the bonding interface, which presented a higher bonding strength than copper. Some dimples and tearing edges with different sizes on the fracture surfaces, indicating that the fracture was a typical ductile fracture.

Novel antenna array configuration using miniature double box branch‐line couplers for wideband circularly polarised applications

AbstractThis article presents a wideband circularly polarised (CP) antenna array using a miniaturised double box branch‐line coupler. This was achieved by creating a slow wave structure by introducing open‐circuit stubs on the inside arms of the branch‐line coupler. The 2 × 2 antenna array is made of four CP slot radiating elements excited through 1 × 4 feeding network. Moreover, sequentially rotation method is used to increase the axial‐ratio (AR) bandwidth of the array. The CP slot radiating element is fed by coplanar waveguide. The feedline of the horn‐shaped radiator includes a circular matching stub. Ground connected asymmetric T‐shaped stub, a pair of grounded L‐shaped square strips, and single strip line are shown to induce CP and enhance the antenna's 3 dB impedance bandwidth and AR performance. The antenna constituting the array has impedance bandwidth of 2.45 GHz from 4.8 to 7.25 GHz that corresponds to a fractional bandwidth of 40%, and its 3 dB AR extends between 4.8 and 6.25 GHz. Compared to a conventional double‐box branch‐line coupler the size of the proposed coupler is reduced by 35% by increasing the capacitance of the coupler's arms. This also is shown to increase the impedance bandwidth of the coupler. A 2 × 2 array was fabricated, and its performance verified. Measured results confirm the proposed antenna array exhibits CP covering the bands of WiMAX IEEE 802.16, C‐band and ITU‐R F386.9. The measured 3 dB AR bandwidth of the antenna array extend from 3 to 7.3 GHz and its impedance bandwidth extends from 3.2 to 9.0 GHz. The antenna array radiates with a peak gain of 11.5 dBic.

Analisis Simple Cell, Twin Cell, dan Tripple Cell Box Culvert Menggunakan Software Ansys

Box culverts are part of a low-rise structure used to convey water in appropriate channels at railroad crossings, flyovers, roads and bridges. The use of box culverts is according to their function, the amount of damage to box culverts is wrong because the functions and loads that can hold the box culverts are also not taken into account. Any force given to the load affects the behavior of the structure contained in the box culvert. IRC is a loading determination that will be given to the box culvert to see the worst structural behavior that occurs. 2D and 3D modeling was carried out using SAP2000 and Ansys Workbench software with the dimensions of the box culvert model measuring 1000 x 1000 x 160 mm and 3 types, namely single box culvert, double box culvert and triple box culvert. The loading on the box culvert is in the form of a divided and evenly distributed load with a loading value in accordance with the provisions of IRC Class A. The box culvert modeling has a quality of 35 MPa and is designed with several types of loading placement on a single box culvert, double box culvert and triple box culvert structure. culvert with an evenly distributed load of 0.205 mm at maximum loading and a maximum moment of 41.988 KN, under maximum loading conditions planned support reinforcement 17D16-250 and 5D16-250 and stirrups D13-250.

DESIGN OF A 10 TONS OVERHEAD CRANE WITH 21 METERS SPAN USING FINITE ELEMENT METHOD

A crane is a lifting equipment widely used to move cargo, construction sites, storage, and unload. The type of crane that is commonly used in industrial environments is the overhead crane. The overhead crane functions as a lifting device. Besides that, it also works as a load transfer tool even though the load being moved is limited to an environment that is not too large (indoor) at PT. A overhead crane is designed to overcome the problem of moving material in the mold storage area due to the area's expansion and the addition of 5-7 tons of mold material. Therefore, proper design is needed so the overhead crane can function properly. The design method uses the VDI 2221 or Finite Element with Solid works software. The results of the structure obtained are double box girder type girders with dimensions p = 21 m, t = 1224 mm, and l = 600 mm. The deflection results are 13.75 mm, and the runway uses steel profile I with dimensions 400 x 200 x 8 x 13 mm, with a deflection value at the runway stem of 5.6 mm. The type of wire rope used is type 6 x 37, with a diameter of 28 mm. The stress that occurs in the steel rope is 4306.1 Kg, less than the maximum allowable tensile stress of 8009.4 Kg. The single hook type with a hook diameter of 120 mm is made of material S45C. The tensile stress on the hook is 0.88 Kg, and the result is smaller than the allowable tensile stress of 12.72 Kg. The pulley diameter is 630 mm, the drum diameter is 604.9 mm, and the drum length is 279 mm.

An infinite family of elliptic ladder integrals

We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of these families can also be written as a dlog form. For both families of diagrams, we provide new 2ℓ-fold integral representations that are linearly reducible in all but one variable and that make the above properties manifest. We illustrate the simplicity of this integral representation by directly integrating the three-loop representative of both families of diagrams. These families also satisfy a pair of second-order differential equations, making them ideal examples on which to develop bootstrap techniques involving elliptic symbol letters at high loop orders.

The massless non-adjacent double off-shell scalar box integral — branch cut structure and all-order epsilon expansion

We generalize the result of our recent paper on the massless single off-shell scalar box integral to the case of two non-adjacent end points off the light cone. An analytic result in d = 4 − 2ε dimensions is established in terms of four Gauss hypergeometric 2F1 functions respectively their single-valued counterparts. This allows for an explicit splitting of real and imaginary parts, as well as an all-order ε-expansion in terms of single-valued polylogarithms.

Shaping Effects on Long Span Bridge Deck Aerodynamics

An aerodynamic circumstance of wind pressure surrounding the long-span bridge allocates many theoretical and experimental research to this topic. Determination of the materials and optimal cross-sectional shape of bridge decks that affected a dynamic behavior of long span bridge deck is still included in current research issues and works to be continued in this path. These include the Lack of sufficient awareness of wind forces, stemming from complex nature, and the unpredictability of the wind nature. In this study, in addition to recognizing the aerodynamic behavior of the flutter, the acting pressure forces on the bridge deck are investigated. The geometrical shape of decks, wind velocity, and flutter conditions are adopted as design variables that affected the dynamic forces exerted on bridge decks. A common type of geometric sections of the long-span bridge deck and effective aerodynamic phenomena are examined. The hollow box steel suspended deck and double cells box girder linked via upper flanges and cells linked via the top and bottom flanges are adopted for Computational Fluid Dynamic (CFD) approach. Thus, aerodynamic instability and turbulent torsional flutter flows, as well as a trail of shedding vortices around the bridge decks, are investigated. By changing some geometrical parameters of commonly used bridge sections, the optimal cross-section in terms of turbulence created above and below the deck section is examined and an optimal cross-sectional shape variable is proposed. The shape variable and section dimensions adopted for CFD-Simulations are similar to the dimensions and materials used in previous laboratory specimens of wind tunnels to be able to interpret the results and possibly verify them with the result of the current study.

Feynman integrals for binary systems of black holes

The initial phase of the inspiral process of a binary black-hole system can be described by perturbation theory. At the third post-Minkowskian order a two-loop double box graph, known as H-graph, contributes. In this talk we report how all master integrals of the H-graph with equal masses can be expressed up to weight four in terms of multiple polylogarithms. We also discuss techniques for the unequal mass case. The essential complication (and the focus of the talk) is the occurrence of several square roots.

The diagrammatic coaction and cuts of the double box

The diagrammatic coaction encodes the analytic structure of Feynman integrals by mapping any given Feynman diagram into a tensor product of diagrams defined by contractions and cuts of the original diagram. Feynman integrals evaluate to generalized hypergeometric functions in dimensional regularization. Establishing the coaction on this type of functions has helped formulating and checking the diagrammatic coaction of certain two-loop integrals. In this talk we study its application on the fully-massless double-box diagram. We make use of differential equation techniques, which, together with the properties of homology and cohomology theory of the resulting hypergeometric functions, allow us to formulate the coaction on a range of cuts of the double box in closed form.

SAMPL9 blind predictions using nonequilibrium alchemical approaches.

We present our blind predictions for the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL), ninth challenge, focusing on the binding of WP6 (carboxy-pillar[6]arene) with ammonium/diammonium cationic guests. Host-guest binding free energies have been calculated using the recently developed virtual double system single box approach, based on the enhanced sampling of the bound and unbound end-states followed by fast switching nonequilibrium alchemical simulations [M. Macchiagodena et al., J. Chem. Theory Comput. 16, 7160 (2020)]. As far as Pearson and Kendall coefficients are concerned, performances were acceptable and, in general, better than those we submitted for calixarenes, cucurbituril-like open cavitand, and beta-cyclodextrines in previous SAMPL host-guest challenges, confirming the reliability of nonequilibrium approaches for absolute binding free energy calculations. In comparison with previous submissions, we found a rather large mean signed error that we attribute to the way the finite charge correction was addressed through the assumption of a neutralizing background plasma.

Assessment of Mtn Lumos Box Solar Energy as an Alternative Source of Electricity Power Supply in Nigeria: Case Study of Mubi, Adamawa State North Eastern Nigeria

This research was carried out in Mubi, Adamawa State North Eastern Nigeria. Mubi lie within latitude 10 0015ꞌN and 100 025ꞌN and longitude 130 015 ꞌE and 130 025 ꞌE. The research was aimed at accessing the MTN Lumos box solar energy as an alternative source of electricity power supply with the purpose of having another source of electric power supply in Nigeria, off the National grid and discourages the uses of electric power generator due to high cost of fueling and maintenance. The equipment’s were connected properly according to the manual specifications; the equipment’s includes the following: the solar panel, cable, MTN Lumos box, inverter 60W, LED bulbs and a Television LG 32 inch. The research was carried out in six days: 24th August, 2021, 26th August, 2021, 30th August, 2021, 23rd December,2021, 24th December, 2021 and 28th December, 2021. These six days the MTN Lumos box battery was allowed to charge to 100% and 74% minimum. From the experiment and the result obtained, it was observed that the solar energy conversion system supply electricity power for three hours twenty minutes to the low power consumption house hold electric appliances uninterrupted, double panel MTN Lumos box electricity power supply should be used for further research.

SAMPL9 blind predictions using nonequilibrium alchemical approaches

We present our blind predictions for the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL), 9th challenge, focusing on binding of WP6 (carboxy-pillar[6]arene) with ammonium/diammonium cationic guests. Host-guest binding free energies have been calculated using the recently developed virtual double system single box approach, based on the enhanced sampling of the bound and unbound end-states followed by fast switching nonequilibrium alchemical simulations [M Macchiagodena, M Pagliai, M Karrenbrock, G Guarnieri, F Iannone, Procacci, J Chem Theory Comput, 16, 7260, 2020]. As far as Pearson and Kendall coefficients are concerned, performances were acceptable and, in general, better than those we submitted for calixarenes, cucurbituril-like open cavitand, and beta-cyclodextrines in previous SAMPL host-guest challenges, confirming the reliability of nonequilibrium approaches for absolute binding free energy calculations. In comparison with previous submissions, we found, nonetheless, a rather large mean signed error that we attribute to the way the finite charge correction was addressed through the assumption of a neutralizing background plasma.

Analysis of Tube-to-Tubesheet Welding in Carbon Steel Heat Exchangers of a Double Plate Header Box.

The rear wall of the header box serves as a tubesheet in heat exchangers of double plate header box. Tube-to-tubesheet welding must be performed using orbital Gas Tungsten Arc Welding (GTAW) with a head extension, which is passed through the corresponding hole in the front wall (plugsheet) of the header box, where the welding machine is supported. In this project, the effect of parallelism deviations between the plugsheet and the tubesheet of carbon steel header box is analyzed to evaluate its influence on the quality of the tube-to-tubesheet welding. Welded tube (SA-210 Gr. A1) to tubesheet (SA-516 Gr. 70) coupons are manufactured simulating the parallelism deviations previously analyzed in two double plate header boxes of air-cooled heat exchangers using two different preheating temperatures. Macrographic analysis is performed in order to evaluate the weld penetration (minimum leak path) and length of the weld leg in tube-to-tubesheet joints. The results obtained show important variations in those parameters when the parallelism deviations are equal to or greater than −1 mm over the theoretical distance as well as when the distance approaches +1 mm or more. Finally, the incorporation of dimensional controls prior to the welding process is discussed and the implementation of improvements in orbital GTAW equipment is recommended as an optimal solution for this kind of heat exchangers.