Two-dimensional Setting Research Articles

On sequences of convex records in the plane

Abstract Convex records have an appealing purely geometric definition. In a sequence of d-dimensional data points, the nth point is a convex record if it lies outside the convex hull of all preceding points. We specifically focus on the bivariate (i.e. two-dimensional) setting. For iid (independent and identically distributed) points, we establish an identity relating the mean number ⟨ R n ⟩ of convex records up to time n to the mean number ⟨ N n ⟩ of vertices in the convex hull of the first n points. By combining this identity with extensive numerical simulations, we provide a comprehensive overview of the statistics of convex records for various examples of iid data points in the plane: uniform points in the square and in the disk, Gaussian points and points with an isotropic power-law distribution. In all these cases, the mean values and variances of Nn and Rn grow proportionally to each other, resulting in the finite limit Fano factors FN and FR . We also consider planar random walks, i.e. sequences of points with iid increments. For both the Pearson walk in the continuum and the Pólya walk on a lattice, we characterise the growth of the mean number ⟨ R n ⟩ of convex records and demonstrate that the ratio R n / ⟨ R n ⟩ keeps fluctuating with a universal limit distribution.

Singular limit of a chemotaxis model with indirect signal production and phenotype switching

Abstract Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous justification of formal computations performed in the literature. The expected limit system being the classical parabolic–parabolic Keller–Segel system, the obtained convergence is restricted to a finite time interval for general initial conditions but valid for arbitrary bounded time intervals when the mass of the initial condition is appropriately small. Furthermore, if the solution to the limit system blows up in finite time, then neither of the two phenotypes in the partially diffusive system can be uniformly bounded with respect to the L 2-norm beyond that time.

Turbulent flame acceleration and deflagration-to-detonation transitions in ethane–air mixture

The deflagration-to-detonation transition (DDT) poses significant risks in the oil, gas, and nuclear industries, capable of causing catastrophic explosions and extensive damage. This study addresses a critical knowledge gap in understanding the DDT of ethane–air mixtures on a large scale, amid increasing industrial utilization and production of ethane. A novel computational framework is introduced, utilizing the finite-volume code named Morris Garages, which incorporates reactive compressible Navier–Stokes equations, adaptive mesh refinement, and correlations of turbulent burning velocities. This model integrates the most recent data on laminar and turbulent burning velocities for premixed ethane–air mixtures, simulating flame acceleration and DDT within a two-dimensional large-scale setting, measuring 21 m in length and 3 m in height, with obstacles mimicking pipe congestion. Two mixture scenarios, lean and near-stoichiometric, are analyzed to evaluate the effects of equivalence ratios on flame propagation and DDT. The simulations, validated against large-scale experimental data from Shell, show reasonable agreement and provide critical insights into the onset conditions of DDT, such as temperature, pressure, flame speed, and turbulent kinetic energy. Furthermore, the ξ–ε detonation peninsula diagram is utilized to explore autoignition and detonation behaviors in ethane–air mixtures.

A Computational Design Framework for Lubrication Interfaces With Active Micro-textures

Abstract The major goal of the present study is to develop a computational design framework for the active control of hydrodynamically lubricated interfaces. The framework ultimately delivers an electrode distribution on an elastomeric substrate such that a voltage-controlled texture may be induced on its surface. This enables the setup to attain a desired time-dependent macroscopic lubrication response. The computational framework is based on a numerically efficient two-stage design approach. In the first stage, a topology optimization framework is introduced for determining a microscopic texture and the uniform modulation of its amplitude. The objective is to attain the targeted fluid flux or frictional traction signals based on the homogenization-based macroscopic response of the texture. As a minor goal, a novel unit cell geometry optimization feature will be developed which will enable working in a design space that is as unrestricted as possible. The obtained designs are then transferred to the second stage where the electrode distribution on a soft substrate is determined along with the voltage variation that delivers the desired amplitude variation. The first stage operates in a two-dimensional setting based on the Reynolds equation whereas the second stage operates in a three-dimensional setting based on an electroelasticity formulation. The two stages are heuristically coupled by transferring the texture topology to the electrode distribution through a projection step. The viability of such an active lubrication interface design approach is demonstrated through numerous examples that methodically investigate the central features of the overall computational framework.

Effect of Human Interaction Modalities on the Usability and Performance of a Robotic Cyber-Physical System for Construction Progress Monitoring

The construction industry has been slow to adopt advanced technologies like Cyber-Physical Systems (CPS), underscoring the necessity for a human-centered approach to their development. This study aims to understand the significance and impact of human-CPS interaction modalities on human perceptions of CPS, specifically in the use case of construction progress monitoring. A mixed-method approach comprising quantitative observations and qualitative interviews was employed to evaluate the system’s usability and performance with different human-CPS interaction modalities. The findings reveal variable levels of usability and performance across different human-CPS interaction modalities. Users expressed a preference for the three-dimensional immersive environment compared to a two-dimensional setting due to a better sense of presence. However, they experienced heightened cognitive load when utilizing novel interaction methods such as hand gestures and voice commands. Interestingly, despite this increased cognitive demand, users exhibited comparable performance in the assigned task, irrespective of their familiarity with the interaction modality. The results underscore the importance of human-centered design in CPS development. It contributes empirical evidence crucial for understanding and improving human-CPS interactions, thereby advancing the implementation of CPS in construction progress monitoring.

Modified error-in-constitutive-relation (MECR) framework for the characterization of linear viscoelastic solids

We develop an error-in-constitutive-relation (ECR) approach toward the full-field characterization of linear viscoelastic solids described within the framework of standard generalized materials. To this end, we formulate the viscoelastic behavior in terms of the (Helmholtz) free energy potential and a dissipation potential. Assuming the availability of full-field interior kinematic data, the constitutive mismatch between the kinematic quantities (strains and internal thermodynamic variables) and their “stress” counterparts (Cauchy stress tensor and that of thermodynamic tensions), commonly referred to as the ECR functional, is established with the aid of Legendre–Fenchel gap functionals linking the thermodynamic potentials to their energetic conjugates. We then proceed by introducing the modified ECR (MECR) functional as a linear combination between its ECR parent and the kinematic data misfit, computed for a trial set of constitutive parameters. The affiliated stationarity conditions then yield two coupled evolution problems, namely (i) the forward evolution problem for the (trial) displacement field driven by the constitutive mismatch, and (ii) the backward evolution problem for the adjoint field driven by the data mismatch. This allows us to establish compact expressions for the MECR functional and its gradient with respect to the viscoelastic constitutive parameters. For generality, the formulation is established assuming both time-domain (i.e. transient) and frequency-domain data. We illustrate the developments in a two-dimensional setting by pursuing the multi-frequency MECR reconstruction of (i) piecewise-homogeneous standard linear solid, and (b) smoothly-varying Jeffreys viscoelastic material.

A Novel Generalized n-Dimensions Sixtic B-Spline Function to Solving n-Dimensions Mathematical Models

In this study, we present a novel framework for the sixtic B-spline collocation approach in n-dimensions. Building upon previous research that focused on developing B-spline functions in n-dimensions to solve mathematical models, this work represents an extension of those efforts. We provide formulations of the sixtic B-spline collocation algorithm in one-dimensional, two-dimensional, and three-dimensional settings. These structures play a crucial role in solving mathematical models across diverse fields of study. To showcase the efficacy and accuracy of the proposed method, we employ a range of test problems in two and three dimensions. These examples serve as demonstrations of the effectiveness and precision of the suggested approach.

Inner autoequivalences in general and those of monoidal categories in particular

We develop a general theory of (extended) inner autoequivalences of objects of any 2-category, generalizing the theory of isotropy groups to the 2-categorical setting. We show how dense subcategories let one compute isotropy in the presence of binary coproducts, unifying various known one-dimensional results and providing tractable computational tools in the two-dimensional setting. In particular, we show that the isotropy 2-group of a monoidal category coincides with its Picard 2-group, i.e., the 2-group on its weakly invertible objects.

Optimal distributed control for a Cahn-Hilliard-Darcy system with mass sources, unmatched viscosities and singular potential

We study a Cahn-Hilliard-Darcy system with mass sources, which can be considered as a basic, though simplified, diffuse interface model for the evolution of tumor growth. This system is equipped with an impermeability condition for the averaged velocity u as well as homogeneous Neumann boundary conditions for the phase function ϕ and the chemical potential µ. The source term in the convective Cahn-Hilliard equation contains a control R that can be thought as a drug or a nutrient in applications. Our goal is to study a distributed optimal control problem in the two-dimensional setting with a cost functional of tracking-type. In the physically relevant case with unmatched viscosities for the binary fluid mixtures and a singular potential, we first prove the existence and uniqueness of a global strong solution with ϕ being strictly separated from the pure phases ±1. This well-posedness result enables us to characterize the control-to-state mapping S: R→ϕ. Then we obtain the existence of an optimal control, the Frechet differentiability of S and first-order necessary optimality conditions expressed through a suitable variational inequality for the adjoint variables. Finally, we prove the differentiability of the control-to-costate operator and establish a second-order sufficient condition for the strict local optimality.

Formation and propagation of fundamental and vortex soliton families in 1D and 2D dual-Lévy-index fractional nonlinear Schrödinger equations with cubic–quintic nonlinearity

We address effects of interplay of two different fractional-diffraction terms, corresponding to different Lé vy indices (LIs), in the framework of nonlinear Schrödinger equation (NLSE) with cubic–quintic nonlinearity (dual-LI fractional NLSE ), in one- and two-dimensional (1D and 2D) settings. The critical (in 1D) and supercritical (in 2D) wave collapses are suppressed in the presence of a defocusing quintic term, making it possible to produce stable localized modes, including fundamental and vortical ones. In 2D, families of fundamental and vortex solitons, with topological charges S=0,1,2,3, are produced in a numerical form and by dint of the variational approximation (VA). In particular, the threshold power necessary for the existence of 2D fundamental solitons is predicted by the VA, being close to the numerical results. In the case of fractional-diffraction terms with unequal LIs acting in two transverse directions, anisotropic 2D fundamental and vortex solitons are constructed. Stability of the solitons is investigated for small perturbations governed by the linearized equations, and results are corroborated by direct simulations of the perturbed evolution. Those vortex solitons which are unstable are split by azimuthal perturbations into fragments, whose number is determined by the shape of the perturbation eigenmode with the largest growth rate. These results extend the concept of the 2D fractional diffraction and solitons to media with the anisotropic fractionality.

Impact of Blade Modifications on the Performance of a Darrieus Wind Turbine

Vertical axis wind turbines (VAWTs) are gaining increasing significance in the realm of renewable energy. One notable advantage they possess is their ability to operate efficiently in diverse wind conditions, including low-speed and turbulent winds, which are often prevalent in urban areas. In this study, dimples and pitch angles into the rotor blades are used to enhance the aerodynamic performance of a straight-bladed Darrieus turbine. To simulate the turbine’s rotation under transient conditions, computational fluid dynamics calculations are conducted in a two-dimensional setting. The unsteady Navier–Stokes equations are solved, and the k-ω SST turbulence model is employed to represent turbulent flow. The results of the simulation demonstrate that the application of a circular dimple on the pressure side of the blades, positioned at 0.25 of the chord length with a diameter of 0.08 chord length, leads to a 5.18% increase in the power coefficient at λ = 2.7, in comparison to a turbine with plain airfoils. Moreover, when an airfoil with both a dimple and a + 1° pitch angle is utilized, the turbine’s performance at λ = 2.7 improved by 7.17% compared to a plain airfoil, and by 1.8% compared to a dimpled airfoil without a pitch angle. Additionally, the impact of a double dimple on both the pressure and suction sides of the airfoil on turbine performance was investigated. It was discovered that the double-dimpled airfoil exhibited lower performance in comparison to a plain airfoil. The study showed that the utilization of both dimples and pitch angles for airfoils of a Darrieus turbine blade increases the power generated by the turbine.

Abstract 577: Deciphering the mechanism of the menin-MLL complex dependency in HCC

Abstract Liver cancer is the third leading cause of cancer-related death worldwide, with hepatocellular carcinoma (HCC) being the most common primary liver cancer (~90%). The 5-year survival rate of patients with advanced HCC is ~18% due to the late prognosis and the moderate clinical benefit of available systemic therapy options. Mutations in chromatin regulators were detected in ~50% of liver cancer. Since many chromatin regulators have been shown a dependency in various cancer types and can modulate therapy response, we focused on identifying new therapeutic targets of HCC among epigenetic modifiers and evaluating them as potential targets for future drug development. We constructed a CRISPR library of 6000 gRNAs targeting 737 genes involved in chromatin-mediated gene regulation. Using the epigenome-focused CRISPR/Cas9 screening in two-dimensional and three-dimensional settings in multiple liver cancer cell lines (HepG2, HLF, PLC/PRF5), we identified a list of epigenetic regulators as potential new targets in HCC. Two of them, MEN1 and ASH2L, are core subunits of the menin-MLL complex mediating H3K4 trimethylation (me3). We validated dependencies of HCC on MEN1 and ASH2L by performing a negative selection CRISPR/Cas9 competitive growth assay in HLF and PLC/PRF5 cell lines. Moreover, treatment of HCC cell lines (HLF, PLC/PRF5, HepG2) with recently developed menin inhibitor SNDX-5613 (revumenib) revealed a dose-dependent reduction in cell proliferation. To determine transcriptional changes associated with disruption of the menin-MLL complex, we performed RNA sequencing of HLF and PLC/PRF5 cells following either inhibition with 5µM SNDX-5613 for 4 days or knockout of the MEN1 or ASH2L gene. We observed the upregulation of KRAS and the oncogenic signature of TGFβ signaling pathways in all menin-MLL complex disrupting conditions. We did not detect global changes in H3K4me3 levels upon the menin inhibition or MEN1 or ASH2L knockouts assessed by immunoblotting. To explore the mechanism of the antiproliferative effect of the menin inhibition on HCC further, we evaluated changes in the binding of menin to chromatin and H3K4me3 levels in HCC cells by performing CUT&RUN following treatment of HLF cells with 5µM SNDX-5613 for 4 days. Menin inhibition led to a drastic removal of menin from the chromatin, while H3K4me3 levels were only mildly decreased. We identified 8765 genes near promoter regions with menin binding and H3K4me3 mark, of which 1952 genes were near regions with simultaneous loss of menin and decreased H3K4me3 levels upon menin inhibition. Integration of our genomics data revealed a list of 30 genes, which are downregulated upon menin inhibition in both HLF and PLC/PRF5 cells (FC≥1.5) and the direct targets of the menin-MLL complex in HLF cells, suggesting their potential role in HCC cell survival. Altogether, we anticipate that menin and ASH2L serve as promising targets and represent an appealing therapeutic strategy for HCC treatment. Citation Format: Margarita M. Dzama, Peyton C. Kuhlers, Jesse R. Raab. Deciphering the mechanism of the menin-MLL complex dependency in HCC [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 577.

The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions

A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by Elgindi and Rousset (2015) where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by Bhave et al. (1991), since the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present work, we obtain the global-in-time existence and uniqueness of the strong solution to the non-diffusive model with small initial data by deriving some uniform regularity estimates and taking vanishing diffusion limits. In addition, the large time behavior of the solution is studied and the optimal time-decay rates for each order of spatial derivatives are obtained. The main challenges focus on the lack of dissipation and regularity effects of the system and on the slower decay in the two-dimensional settings. A combination of the spectral analysis and the Fourier splitting method is adopted.

Analysis of the linearly extrapolated BDF2 fully discrete Modular Grad-div stabilization method for the micropolar Navier-Stokes equations

<abstract><p>We investigate a fully discrete modular grad-div (MGD) stabilization algorithm for solving the incompressible micropolar Navier-Stokes equations (IMNSE) model, which couples the incompressible Navier-Stokes equations and the angular momentum equation together. The mixed finite element (FE) method is applied for the spatial discretization. The time discretization is based on the BDF2 implicit scheme for the linear terms and the two-step linearly extrapolated scheme for the convective terms. The considered algorithm constitutes two steps, which involve a post-processing step for linear velocity. First, we decouple the fully coupled IMNSE model into two smaller sub-physics problems at each time step (one is for the linear velocity and pressure, the other is for the angular velocity), which reduces the size of the linear systems to be solved and allows for parallel computing of the two sub-physics problems. Then, in the post-processing step, we only need to solve a symmetrical positive determined grad-div system of linear velocity at each time step, which does not increase the computational complexity by much. However, the post-processing step can improve the solution quality of linear velocity. Moreover, we obtain unconditional stability, and error estimates of the linear velocity and angular velocity. Finally, several numerical experiments involving three-dimensional and two-dimensional settings are used to validate the theoretical findings and demonstrate the benefits of the modular grad-div (MGD) stabilization algorithm.</p></abstract>

Di-orthographs of Banach spaces that are not invariant of nonlinear Birkhoff-James orthogonality preservers

In this paper, we study the relationship between two known nonlinear equivalences of normed spaces induced by Birkhoff-James orthogonality. To be precise, we consider the nonlinear equivalences of normed spaces with respect to the structure of Birkhoff-James orthogonality and di-orthographs of them. It is shown that a graph isomorphism between di-orthographs of normed spaces gives rise to a Birkhoff-James orthogonality preserver, but the converse is false in general. A counterexample is constructed in the real two-dimensional setting. Radon planes and a reduced version of di-orthographs play important roles in this direction.

Жанрове розмаїття «п’єси у п’єсі» в сучасній українській літературі

The problem of studying the evolution of ironical element in literature is crucially important and relevant. This article deals with the ironical style in dramaturgy, owing to the fact that it is founded on the element of game intrinsic to irony. The rhetoric figure of pretension (eironeia), from which the mentioned kind of comical had initiated, conditions the main object for this research — «a theatre within a theatre», or «a stage within a stage». Two-dimensional setting of the action (both in formal and substantial aspects) serves as an impetus for development of an ironic style not only in a play, but also in any possible generic modifications of this structure. In other words, an array of literary works shares the same artistic code, upon being included into the single play. Therefore, the main formal factor in this case is «a rehearsal», on which either an entire play or its part gets based. Actually, the studies of «a stage within a stage» in Ukrainian literature remain relevant nowadays. Regarding the history of national dramatic art, it can be said that there were few «rehearsal plays» and «show plays» in Ukraine for the time being; works like «Spokusy nesviatogo Antona (Temptations of Unholy Anthon)» by Ihor Kostetsky, «Kain (Cain)» by Olha Kyrylova and «Tsyrk zhyttia nashogo (The Circus of Our Life)» by Svitlana Leliukh are the updated epitomes of this genre. On the other hand, it is quite interesting to search for plays with traces of «a stage within a stage», since the functions of this means go far beyond the typical derision of internal theatrical drawbacks and intrigues. Having emerged as a reflection of the theatrical scene, «a stage within a stage» can evolve in any closed and open space. Significantly, this symbolizes the movement towards the event elements of theatrical action itself; however (when it comes to a high-quality artistic work), in case of showing some extraordinary events that set up acute conflicts either to be solved or remain open during the action.

IMPROVING CHARACTERISTICS OF THE IMPELLER OF A HIGH-PRESSURE CENTRIFUGAL COMPRESSOR BY DESIGNING WITH THE HELP OF CAD

High-pressure compressors are among the most common pneumatic machines in industry and transport. Classical methods of designing such machines are based on flow modeling methods in two-dimensional and one-dimensional settings. The specified design methods lead to the creation of sufficiently perfect constructions, but their characteristics can still be improved. To simulate the flow in a high-pressure compressor, it becomes relevant to study the possibilities of optimizing the design using the Ansys Vista CAD system, which can significantly increase the efficiency of the compressor. The goal of the work is to improve the characteristics of the high-pressure centrifugal compressor impeller by designing with the help of CAD. The study was carried out on the basis of the design of the flow part of the impeller of a high-pressure centrifugal compressor using the Ansys VistaCCD automated design system based on the operation parameters of a mass-produced compressor. It was found that the efficiency maxima location of the designed and serial compressor impellers are approximately the same, while the polytropic efficiency of the designed impeller is 6 % more. At the same time, the ratio of total pressures decreases by 18 %. On the other hand, the high-efficiency zone of the impeller is significantly expanded for the designed impeller. This range has increased more than three times. At the same time, in the zone of optimal efficiency, the power consumed for the designed impeller decreases by 20 % to 240 kW. The designed impeller has a more perfect distribution of pressures for the splitter with approximately the same characteristics for the main blades of the impellers. Analyzing the velocity vectors and distributions, it can be derived that the serial compressor has two separation zones: in the blade bending region and at the outlet, unlike the designed one.

Global existence of solutions to the 4D attraction–repulsion chemotaxis system and applications of Brezis–Merle inequality

We consider the Cauchy problem for an attraction–repulsion chemotaxis system in the four space dimension. One of main topics in the study of such a system is the presence of L 1 threshold. In fact, the critical mass phenomenon called 8π-problem is well-known in the two-dimensional setting. In this paper, we show the global existence of solutions to the Cauchy problem for the four-dimensional subcritical case, that is, the total mass of the initial data is less than the four-dimensional L 1 threshold value . The key ingredients are the four-dimensional Brezis–Merle type inequality of the 4th-order elliptic equation and some inequalities derived from rearrangement arguments.

Generalised solution to a 2D parabolic-parabolic chemotaxis system for urban crime: Global existence and large-time behaviour

AbstractWe consider a parabolic-parabolic chemotaxis system with singular chemotactic sensitivity and source functions, which is originally introduced by Short et al to model the spatio-temporal behaviour of urban criminal activities with the particular value of the chemotactic sensitivity parameter $\chi =2$ . The available analytical findings for this urban crime model including $\chi =2$ are restricted either to one-dimensional setting, or to initial data and source functions with appropriate smallness, or to initial data and source functions with some radial symmetry. In the present work, our first result asserts that for any $\chi \gt 0$ the initial-boundary value problem of this urban crime model possesses a global generalised solution in the two-dimensional setting, without imposing any small or radial conditions on initial data and source functions. Our second result presents the asymptotic behaviour of such solution, under some additional assumptions on source functions.

On regularization results for a two-dimensional nonlinear time-fractional inverse diffusion problem

Ill-posed inverse problems arise in a variety of practically important applications including image restoration, medicine, ecology as well as many other branches of pure and applied sciences. In this paper, we consider an ill-posed inverse problem for a two-dimensional nonlinear time-fractional inverse diffusion model involving the Caputo time-fractional derivative as follows:{Dtβu(x,y,t)=−a(x)(ux(x,y,t)+uy(x,y,t))+ℓ(x,y,t,u(x,y,t)),x>0,y>0,t>0,u(x,y,0)=0,x>0,y>0,limx→∞⁡u(x,y,t)=0,y>0,t>0,u(1,y,t)=u1(y,t),y>0,t>0, where β∈(0,1) is fixed, a is a space-dependent diffusion coefficient, ℓ is a nonlinear function satisfying a Lipschitz condition, and the data u1 is given approximately. We want to determine u(x,y,t) for 0≤x<1. There exists a vast literature on regularization results related to the considered problem. We are concerned with regularization results for the nonlinear case. The first regularization results in such a case were studied by Tuan, Hoan and Tatar in [17]. While these results apply to a constant diffusivity coefficient in the one-dimensional setting, the results of Vo and co-worker in [18], more generally, apply to the case of the space-dependent diffusion coefficient in the two-dimensional setting. In all these papers relatively strong a priori assumptions on the regularity of the exact solution are made. In this work, we weaken such a priori assumptions via two regularization strategies based on the integral equation method. We obtain several explicit error estimates including an error estimate of the Hölder-Logarithmic type for all x∈[0,1), which can be seen as the improvement and the generalization of error estimates presented by Zheng and Wei in [20,21]. Eventually, several numerical examples are presented for the purpose of illustrating the theoretical results.