Common Boundary Research Articles

A-optimal experimental designs for Michaelis – Menten model

Kinetics of simple and complex kinetic reactions is usually described by exponential and rational models. The fractional rational models include the well-known Michaelis – Menten model of enzymatic kinetics. In the presented article A-optimal designs are proposed for the Michaelis – Menten model. The elimination method used to construct A-optimal designs, allowed us to determine the nodes and weights of A-optimal designs separately and thereby extend this approach to other criteria and models of the rational type. It is shown that the nodes of A-optimal designs determined by this method are the roots of the 4th degree algebraic equation with coefficients depending on the model parameters. If the nodes of the A-optimal design are already known, then the weights of the corresponding nodes are determined analytically by the Pukelsheim formula. The properties of the roots as well as the properties of the nodes of A-optimal designs were studied using the Sturm system constructed in the general form for the resulting equation. It is shown that with a certain combination of parameters of the Michaelis – Menten model, the degree of the resulting algebraic equation is reduced to three. A partition of the set of values of the parameters of the Michaelis – Menten model into two subsets has been found. In one of them, the A-optimal design is determined uniquely, whereas for the other one it is necessary to select the optimal node from two possible options. It is revealed that the degree of the algebraic equation is equal to three for points belonging to the curve which is the common boundary of the indicated subsets. Corresponding numerical examples are given to illustrate the results obtained.

Research on digital vibration model of typical components in pipe system

The spatial distribution of pipe system is complex, long span and multi-point elastic support, so vibration analysis of pipe system is required in the pipeline design. This paper takes the pipe system as a typical component, based on the Timoshenko beam model, establishes a dynamic procedure for straight pipe elements that considers the axial flow rate of fluid, the pressure on the pipe wall, the Poisson coupling effect of fluid and pipeline structure, and the axial, transverse and torsional vibration. Through Laplace transform, the frequency simplified dynamic model is established. And the frequency transfer matrix model of straight pipe elements and the boundary constraint matrix of common boundary (such as fixed support) is established. Finally, the frequency domain transfer matrix model of different pipeline elements are set to the overall transfer matrix of the flow pipe system, providing a convenient means for rapid optimization of pipe system vibration.

Simulated hydrogen diffusion in diamond grain boundaries

To evaluate hydrogen diffusion within diamond, a series of molecular dynamics simulations have been carried out in which diffusion coefficients and activation energies were determined. Diamond grown via chemical vapour deposition (CVD) contains a high hydrogen concentration within grain boundaries, because of this, common tilt grain boundaries were recreated from transmission electron microscopy images taken from literature. Diffusion coefficients of hydrogen placed within the grain boundary were estimated and compared to the bulk diffusion. Unlike many crystalline structures, some grain boundaries presented limited diffusion when compared to the bulk. Diffusion characteristics of grain boundaries are thought to be a result of channelling effects combined with the formation of sp3C-H bonds with sp2 carbon present within some grain boundaries - increasing and decreasing diffusion rates respectively. Potential wells were observed across some but not all the grain boundaries resulting in hydrogen trapping and anisotropic diffusion.

The Poisson–Boltzmann equation in micro- and nanofluidics: A formulary

The Poisson–Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with numerous applications ranging from colloid science to biology. This formulary focuses on situations of interest for micro- and nanofluidics, and gathers important formulas for the PB description of a Z:Z electrolyte solution inside slit and cylindrical channels. Different approximated solutions (thin EDLs, no co-ion, Debye–Hückel, and homogeneous/parabolic potential limits) and their range of validity are discussed, together with the full solution for the slit channel. Common boundary conditions are presented, the thermodynamics of the EDL is introduced, and an overview of the application of the PB framework to the description of electrokinetic effects is given. Finally, the limits of the PB framework are briefly discussed, and Python scripts to solve the PB equation numerically are provided.

Spectrum and resolvent of multi-channel systems with internal energies and common boundary conditions

In the article the spectrum and resolvent of the so-called multichannel systems with nonzero internal energies were investigated. The spectrum and resolvent of multichannel Sturm-Liouville systems with non-zero internal energies mi2 and general boundary conditions were investigated. These systems describe the propagation of partial waves in the theory of quantum physics. The importance of studying the spectral characteristics of these systems is presented in the well-known books of the theory of quantum physics. The finiteness of the number of eigenvalues was proved, the multiplicity of positive eigenvalues was investigated, and as well as the resolvent kernel of the system was found.

Microsurgical Anatomy of the Common Tendinous Ring and Its Surgical Implications

BACKGROUND AND OBJECTIVES: The common tendinous ring (CTR), also known as the common annular tendon or annulus of Zinn, is a critical anatomic structure located at the convergence of the orbital apex, superior orbital fissure (SOF), optic canal, and the anterior aspect of the lateral sellar compartment. It plays a vital role in both neurosurgical and neuro-ophthalmological interventions. The aim of this study was to delineate the complex 3-dimensional (3D) topography of the CTR and explore its implications for surgical procedures. METHODS: Ten formalin-fixed skull base specimens from adult Chinese cadavers were meticulously dissected to investigate the morphology of the CTR, focusing particularly on its relationship with the 4 extraocular rectus tendons, the optic strut, the SOF, and the optic canal. Additional skull base specimens were subjected to 3D surface scanning, computed tomography, and histopathological examinations to deepen our understanding of the CTR's structural complexities. RESULTS: The CTR establishes a spatial, 3D tendinous assembly, encompassing 4 rectus tendons, 2 tendinous connections, and a singular common tendinous root. These components interlink to form a distinctive dual-ring configuration, featuring the optic foramen and the oculomotor foramen. The posterior part of the superior rectus tendon demarcates the common boundary between these 2 foramina. The oculomotor foramen itself serves as the central sector of the SOF. Precise incisions of the medial and lateral tendinous connections and fusions are essential for safely opening the CTR. CONCLUSION: The structural composition, interconnections, and dual-ring configuration of the CTR are crucial for precise and safe surgery of orbital apex and adjacent regions.

Parametric surface reconstruction from 3D point data using partial differential equation and bilinearly blended Coons patch

Existing methods for parametric surface reconstruction from 3D point data typically segment the points into multiple subsets, each fitted with a parametric surface patch. These methods face two primary issues. First, they fail to achieve positional continuity between adjacent patches, resulting in gaps or overlaps. Second, parameterizing the data within each subset is a challenging task. In this paper, we address these problems by proposing a novel surface reconstruction method based on Partial differential equation (PDE) deformation surfaces and bilinearly blended Coons patches. Our approach involves first extracting four boundaries for each subset. Next, we generate a bilinearly blended Coons patch from these boundaries. Any errors between the points in the subset and their corresponding points on the Coons patch are minimized or eliminated using a PDE deformation surface, which employs as many unknown constants as necessary to achieve this goal. The proposed method offers several advantages. Firstly, it ensures good positional continuity between adjacent patches, as they share common boundaries. Secondly, reconstruction errors can be easily controlled by adjusting the hyper-parameters in the PDE deformation equation, thereby changing the number of unknown constants as needed. Thirdly, the challenge of point parameterization within each subset is effectively addressed by using the bilinearly blended Coons patch. We validate our method on various datasets of differing complexities and shapes, with results demonstrating the effectiveness and advantages of our approach.

Spectral representation in Klein space: simplifying celestial leaf amplitudes

In this paper, we explore the spectral representation in Klein space, which is the split (2, 2) signature flat spacetime. The Klein space can be foliated into Lorentzian AdS3/ℤ slices, and its identity resolution has continuous and discrete parts. We calculate the identity resolution and the Plancherel measure in these slices. Using the foliation of Klein space into the slices, the identity resolution, and the Plancherel measure in each slice, we compute the spectral representation of the massive bulk-to-bulk propagator in Klein space. It can be expressed as the sum of the product of two massive (or tachyonic) conformal primary wavefunctions, with both continuous and discrete parts, and sharing a common boundary coordinate. An interesting point in Klein space is that, since the identity resolution has discrete and continuous parts, a new type of conformal primary wavefunction naturally arises for the massive (or tachyonic) case. For the conformal primary wavefunctions, both the discrete and continuous parts involve integrating over the common boundary coordinate and the real (or imaginary) mass. The conformal dimension is summed in the discrete part, whereas it is integrated in the continuous part. The spectral representation in Klein space is a computational tool to derive conformal block expansions for celestial amplitudes in Klein space and its building blocks, called celestial leaf amplitudes, by integrating the particle interaction vertex over a single slice of foliation.

A hidden 2d CFT for self-dual Yang-Mills on the celestial sphere

Self-dual Yang-Mills theory admits an underlying infinite dimensional symmetry algebra, which has been obtained from mode expansion of Mellin transformed 4d scattering amplitudes and separately, Koszul duality on twistor space. In this paper, we propose to derive an explicit 2d realization of the algebra by performing a particular gauge transformation on the twistor action for self-dual Yang-Mills. The gauge parameter used in the transformation generates pure gauge connections corresponding to large gauge transformations on 4d Minkowski space, which localises part of the twistor action to a ℂℙ1 on ℂ* reduction of twistor space. Under a projection, it can be mapped to the celestial sphere at the light-cone cut of the origin on I\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{I} $$\\end{document}. Geometrically, this is the common boundary celestial sphere shared by Euclidean AdS3 or Lorentzian dS3 slices of Minkowski space. We comment on the geometric meaning of the derivation from the perspective of minitwistor spaces of the 3d slices embedded in 4d Minkowski space. Using the action functional of this 2d CFT, we compute its stress-energy tensor and central charge. By a further marginal deformation, we calculate correlation functions of current algebra generators purely from the 2d side which reproduce full 4d tree-level form factors.

On the Topology of Surfaces with a Common Boundary and Close DN-Maps

On the Topology of Surfaces with a Common Boundary and Close DN-Maps

Asymptotics for viscous Burgers equation under impulsive forcing

An initial value problem to the viscous Burgers equation under the influence of an external forcing of distribution type is considered. The existence and uniqueness of weak solutions for it are investigated. To do this, we linearize the viscous Burgers equation and show the existence and uniqueness of common boundary function for the associated initial-boundary problems. Jump discontinuity of the spatial derivative of the solution makes a key role in determining large time asymptotics to the solutions. The explicit representation of the common boundary function and its asymptotic behavior are discussed for a specific case of the jump discontinuity. Here, the common boundary is obtained in terms of Associated Legendre functions of the first and second kind. For the general case, asymptotic behavior of the common boundary of the associated initial-boundary problems is used to determine the large time asymptotics for the Cauchy problem to the viscous Burgers equation.

ЭКИНЧИ ТАРТИПТЕГИ ТУУНДУСУНА КАРАТА ЧЕЧИЛБЕГЕН ДИФФЕРЕНЦИАЛДЫК ТЕҢДЕМЕ ҮЧҮН ЧЕКТИК МАСЕЛЕНИН ЧЫГАРЫЛЫШЫН КОЛЛОКАЦИЯ-АСИМПТОТИКАЛЫК МЕТОД МЕНЕН ТАБУУ

Boundary value problems for ordinary differential equations is one of the sections of the general theory of differential equations. The difference between the boundary value problem and the Cauchy problem is that the solution of the differential equation must satisfy boundary conditions connecting the values of the desired function at more than one point. The most common boundary value problem refers to two-point boundary value problems for which boundary conditions are set at two points at the ends of the interval on which solutions are being sought. In addition, the special case of two-point boundary value problems also covers such an important section of the theory of differential equations as the theory of oscillations. In this article, the problem of constructing an asymptotic expansion in a small parameter for solving a boundary value problem for a second-order differential equation of an unresolved relative to the highest derivative of the desired solution is considered. The solution of the boundary value problem is found according to the algorithm of the collocation-asymptotic method. A numerical example of a boundary value problem is considered and an asymptotic decomposition is constructed for solving problems with a relatively small parameter, including the first two terms of the expansions.

Reflection length at infinity in hyperbolic reflection groups

Abstract In a discrete group generated by hyperplane reflections in the 𝑛-dimensional hyperbolic space, the reflection length of an element is the minimal number of hyperplane reflections in the group that suffices to factor the element. For a Coxeter group that arises in this way and does not split into a direct product of spherical and affine reflection groups, the reflection length is unbounded. The action of the Coxeter group induces a tessellation of the hyperbolic space. After fixing a fundamental domain, there exists a bijection between the tiles and the group elements. We describe certain points in the visual boundary of the 𝑛-dimensional hyperbolic space for which every neighbourhood contains tiles of every reflection length. To prove this, we show that two disjoint hyperplanes in the 𝑛-dimensional hyperbolic space without common boundary points have a unique common perpendicular.

The Lebanon-Israel 2022 Maritime Boundary Agreement

Abstract After over a decade of dispute settlement efforts, Israel and Lebanon reached an agreement to establish their common maritime boundary in October 2022. This agreement is a pioneering achievement in the region. It is the first maritime boundary agreement reached between two States that do not have diplomatic relations. The agreement solidifies the trend towards pursuing maritime delimitation and related arrangements over seabed resources in the Eastern Mediterranean Sea. This article analyses the legal nature and content of the Lebanon-Israel 2022 maritime boundary agreement and its implications for the tripoint delimitation of the overlapping maritime areas between Cyprus, Lebanon, and Israel.

USE OF GPR TECHNOLOGIES IN THE ROAD CONSTRUCTION INDUSTRY

The article continues the study on determining the possibility of applying ground penetrating radar (GPR) technologies in the road construction industry. The authors conduct research using an antenna unit that registers the cross-polarisation component of the reflected signal. In this case, processing the obtained radar images comes down to subtracting two mutually orthogonal components of the signal, which allows the determination of areas of the environment with anisotropic properties. Identifying and positioning extraneous inclusions, finding communications, and determining the location of reinforcement in roadway and bridge structures are relevant tasks. Their solution lies in studying the phenomenon of wave diffraction on extraneous inclusions of the investigated environment. Metal inclusions of different diameters are distinctly visible on radar images obtained during laboratory research. The laboratory studies conducted by the authors showed that the shape and nature of the hyperbola of the diffracted wave significantly depend on the object’s depth, diameter, and material. Therefore, further research in this direction should aim at studying the shape of the diffracted wave, which ultimately allows for judging the depth of occurrence and the diameter of a local extraneous inclusion. When finding and identifying reinforcement in structural layers of road surfaces and elements of bridges, difficulties arise due to the spacing of the reinforcing mesh. With a small reinforcing mesh spacing, when the wavelength is longer than the spacing, the reflections from the adjacent reinforcement bars merge into a common continuous boundary and make the lower layers of the structure almost indistinguishable. Solving the mentioned difficulties is possible by improving the equipment base and the algorithms for processing and interpreting the received radar images. Completed theoretical studies and computational experiments allow us to state that the development of road surface thickness measurement and defect detection techniques will become the basis of the road surface monitoring system using the subsurface geolocation method. Keywords: ground penetrating radar, radar image, road surface, dielectric constant, defect detection, thickness measurement, local inclusions.

Wave–structure interaction by a two–way coupling between a fully nonlinear potential flow model and a Navier–Stokes solver

A two-way domain decomposition coupling procedure between a fully nonlinear potential flow model and a Navier–Stokes solver capturing the free surface with a Volume of Fluid method is used to study wave–structure interaction applied to offshore wind turbines. Away from the structure, the large-scale inviscid wave field is modeled by the potential code. Wave generation and absorption in this 3D hybrid model take place in the outer potential domain. The codes exchange data in the region around their common boundaries. Through the two-way coupling, waves propagate in and out of the viscous subdomain, making the hybrid algorithm suitable to study wave diffraction on marine structures, while keeping the viscous subdomain small. Each code uses its own mesh and time step. Subdomains are overlapping, therefore continuity conditions on velocity and free surface have to be verified on two distinct coupling surfaces at any time. Parallel implementation with communications between the models relying on the Message Passing Interface library allows calculations on large spatial and temporal scales. The coupling algorithm is first tested for regular nonlinear waves and then applied to simulate wave loads exerted on a vertical monopile in 3D. Attention is paid to the high-order components of the horizontal force.

Simulating Global Terrestrial Carbon and Nitrogen Biogeochemical Cycles With Implicit and Explicit Representations of Soil Microbial Activity

AbstractNutrient limitation is widespread in terrestrial ecosystems. Accordingly, representations of nitrogen (N) limitation in land models typically dampen rates of terrestrial carbon (C) accrual, compared with C‐only simulations. These previous findings, however, rely on soil biogeochemical models that implicitly represent microbial activity and physiology. Here we present results from a biogeochemical model testbed that allows us to investigate how an explicit versus implicit representation of soil microbial activity, as represented in the MIcrobial‐MIneral Carbon Stabilization (MIMICS) and Carnegie‐Ames‐Stanford Approach (CASA) soil biogeochemical models, respectively, influence plant productivity, and terrestrial C and N fluxes at initialization and over the historical period. When forced with common boundary conditions, larger soil C pools simulated by the MIMICS model reflect longer inferred soil organic matter (SOM) turnover times than those simulated by CASA. At steady state, terrestrial ecosystems experience greater N limitation when using the MIMICS‐CN model, which also increases the inferred SOM turnover time. Over the historical period, however, warming‐induced acceleration of SOM decomposition over high latitude ecosystems increases rates of N mineralization in MIMICS‐CN. This reduces N limitation and results in faster rates of vegetation C accrual. Moreover, as SOM stoichiometry is an emergent property of MIMICS‐CN, we highlight opportunities to deepen understanding of sources of persistent SOM and explore its potential sensitivity to environmental change. Our findings underscore the need to improve understanding and representation of plant and microbial resource allocation and competition in land models that represent coupled biogeochemical cycles under global change scenarios.

On tiling spherical triangles into quadratic subpatches

Various interpolation and approximation methods arising in several practical applications in geometric modeling deal, at a particular step, with the problem of computing suitable rational patches (of low degree) on the unit sphere. Therefore, we are concerned with the construction of a system of spherical triangular patches with prescribed vertices that globally meet along common boundaries. In particular, we investigate various possibilities for tiling a given spherical triangular patch into quadratically parametrizable subpatches. We revisit the condition that the existence of a quadratic parameterization of a spherical triangle is equivalent to the sum of the interior angles of the triangle being π, and then circumvent this limitation by studying alternative scenarios and present constructions of spherical macro-elements of the lowest possible degree. Applications of our method include algorithms relying on the construction of (interpolation) surfaces from prescribed rational normal vector fields.

Exact Results for a Boundary-Driven Double Spin Chain and Resource-Efficient Remote Entanglement Stabilization

We derive an exact solution for the steady state of a setup where two XX-coupled N-qubit spin chains (with possibly nonuniform couplings) are subject to boundary Rabi drives and common boundary loss generated by a waveguide (either bidirectional or unidirectional). For a wide range of parameters, this system has a pure entangled steady state, providing a means for stabilizing remote multiqubit entanglement without the use of squeezed light. Our solution also provides insights into a single boundary-driven dissipative XX spin chain that maps to an interacting fermionic model. The nonequilibrium steady state exhibits surprising correlation effects, including an emergent pairing of hole excitations that arises from dynamically constrained hopping. Our system could be implemented in a number of experimental platforms, including circuit QED. Published by the American Physical Society 2024

Acceleration of computations in modelling of processes in complex objects and systems

The development of methods of parallelization of computing processes, which involve the decomposition of the computational domain, is an urgent task in the modeling of complex objects and systems. Complex objects and systems can contain a large number of elements and interactions. Decomposition allows you to break down a system into simpler subsystems, which simplifies the analysis and management of complexity. By dividing the calculation area of the part, it is possible to perform parallel calculations, which increases the efficiency of calculations and reduces simulation time. Domain decomposition makes it easy to scale the model to work with larger or more detailed systems. With the right choice of decomposition methods, the accuracy of the simulation can be improved, since different parts of the system may have different levels of detail and require appropriate methods of additional analysis. Decomposition allows the simulation to be distributed between different participants or devices, which is relevant for distributed systems or collaborative work on a project. In this work, mathematical models are built, which consist in the construction of iterative procedures for "stitching" several areas into a single whole. The models provide for different complexity of calculation domains, which makes it possible to perform different decomposition approaches, in particular, both overlapping and non-overlapping domain decomposition. The obtained mathematical models of subject domain decomposition can be applied to objects and systems that have different geometric complexity. Domain decomposition models that do not use overlap contain different iterative methods of "stitching" on a common boundary depending on the types of boundary conditions (a condition of the first kind is a Dirichlet condition, or a condition of the second year is a Neumann condition), and domain decomposition models with an overlap of two or more areas consist of the minimization problem for constructing the iterative condition of "stitching" areas. It should be noted that the obtained models will work effectively on all applied tasks that describe the dynamic behavior of objects and their systems, but the high degree of efficiency of one model may be lower than the corresponding the degree of effectiveness of another model, since each task is individual. Keywords: mathematical modelling, decomposition of the computational domain, parallelization, optimization, complex objects and systems.