Finite Dimension Research Articles

An adiabatic boundary condition with cylindrical perfect conductors for improved approximations from heat-pulse measurement near the soil-atmosphere interface

The cylindrical-perfect-conductors (CPC) theory, which assumes an infinite and homogeneous soil medium, can be used to analyze heat pulse (HP) measurements to estimate soil thermal property values. However, when a HP sensor is positioned near the soil surface, the CPC theory is not valid because of the change in media properties at the soil-atmosphere interface. In this study, a CPC solution considering an adiabatic boundary condition (CPC-ABC) is presented to account for the soil-atmosphere interface effect. Compared with the results from numerical simulations, the CPC-ABC solution gave more accurate soil temperature values at the sensing probe than did a CPC model. When a HP sensor was positioned horizontally at a depth of 1 mm below a sand soil surface, the relative errors (RE) of CPC estimated thermal property values were as large as 52%, while the RE values based on the CPC-ABC solution were about 8%. Results from numerical simulations and laboratory experiments both showed that the CPC model worked well for horizontally positioned HP sensors with probe lengths of 70-mm at burial depths greater than 15 mm. Soil-atmosphere interface effect was largely dependent on HP sensor dimensions and measurement volumes. Overall, the extended CPC-ABC theory provided accurate soil thermal property estimates by considering the effects of finite probe properties and the presence of the soil-atmosphere interface.

Dimension of complexes related to special Gorenstein projective precovers (III)

We show that a commutative Noetherian ring R with finite Krull dimension is a Gorenstein ring if and only if Gppd ( X ) = Gpd ( X ) for any complex X of R-modules, where Gpd ( X ) is the Gorenstein projective dimension of X and Gppd ( X ) is the dimension of the complex X related to special Gorenstein projective precovers. In order to do this, the notion of DG-Gorenstein projective resolutions of complexes is introduced and a characterization of Gorenstein projective dimension of complexes is given via DG-Gorenstein projective resolutions.

Neural network learning and Quantum Gravity

The landscape of low-energy effective field theories stemming from string theory is too vast for a systematic exploration. However, the meadows of the string landscape may be fertile ground for the application of machine learning techniques. Employing neural network learning may allow for inferring novel, undiscovered properties that consistent theories in the landscape should possess, or checking conjectural statements about alleged characteristics thereof. The aim of this work is to describe to what extent the string landscape can be explored with neural network-based learning. Our analysis is motivated by recent studies that show that the string landscape is characterized by finiteness properties, emerging from its underlying tame, o-minimal structures. Indeed, employing these results, we illustrate that any low-energy effective theory of string theory is endowed with certain statistical learnability properties. Consequently, several local learning problems therein formulated, including interpolations and multi-class classification problems, can be concretely addressed with machine learning, delivering results with sufficiently high accuracy.

On iso-DICC modules

In this paper, the concept of iso-DICC modules is introduced and extensively investigated. These modules are the generalization of DICC, iso-Noetherian and iso-Artinian modules. We prove that any direct sum of a projective iso-simple and an iso-DICC module is iso-DICC. Unlike DICC rings, we show that iso-DICC rings don’t have finite Goldie dimension, but if R is a semiprime right iso-DICC ring and I is an annihilator ideal of R, then either I or R I has finite Goldie dimension. Furthermore, we investigate the Krull dimension of iso-Noetherian modules and we give an answer to an open problem on this topic. Finally, we generalize some results on semiprime right iso-Artinian rings to a certain class of iso-Artinian modules. We provide sufficient conditions for iso-Artinian modules to have finite Goldie dimension. Also, we show that any semiprime FQS iso-Artinian module, is non-M-singular.

Multiparton Cwebs at five loops

Scattering amplitudes involving multiple partons are plagued with infrared singularities. The soft singularities of the amplitude are captured by the soft function which is defined as the vacuum expectation value of Wilson line correlators. Renormalization properties of soft function allows us to write it as an exponential of the finite soft anomalous dimension. An efficient way to study the soft function is through a set of Feynman diagrams known as Cwebs (webs). We present the mixing matrices and exponentiated colour factors (ECFs) for the Cwebs at five loops that connect six Wilson lines, except those that are related by relabeling of Wilson lines. Further, we express these ECFs in terms of 29 basis colour factors. We also find that this basis can be categorized into two colour structures. Our results are the first key ingredients for the calculation of the soft anomalous dimension at five loops.

On Poisson (2-3)-algebras which are finite-dimensional over the center

One of the classic results of group theory is the so-called Schur theorem. It states that if the central factor-group $G/\zeta(G)$ of a group $G$ is finite, then its derived subgroup $[G,G]$ is also finite. This result has numerous generalizations and modifications in group theory. At the same time, similar investigations were conducted in other algebraic structures, namely in modules, linear groups, topological groups, $n$-groups, associative algebras, Lie algebras, Lie $n$-algebras, Lie rings, Leibniz algebras. In 2021, L.A. Kurdachenko, O.O. Pypka and I.Ya. Subbotin proved an analogue of Schur theorem for Poisson algebras: if the center of the Poisson algebra $P$ has finite codimension, then $P$ includes an ideal $K$ of finite dimension such that $P/K$ is abelian. In this paper, we continue similar studies for another algebraic structure. An analogue of Schur theorem for Poisson (2-3)-algebras is proved.

Adsorption Mechanism and Characteristic Temperatures of the Monolayer Adsorption of CO2 on Graphite: The Role of Graphene Dimensions.

Although simulation results for gaseous adsorption on a surface of infinite extent, modeled with periodic conditions at the boundaries of the simulation box, agree with experimental data at high temperatures, simulated isotherms at temperatures below the triple point temperature show unphysical substeps because of the compromise of interactions within the box and interactions between the box and its mirror image boxes. This has been alleviated with surfaces of finite dimensions (Loi, Q. K.; Colloids Surf., A 2021, 622, 126690 and Castaño Plaza, O.; Langmuir 2023, 39 (21), 7456-7468) to account for free boundaries at the adsorbate patch on the surface, and the critical parameter of this model substrate is the size of the finite surface. If it is too small, the adsorbate patch does not model the physical reality; however, if it is too large, the computation time is excessive, making the simulation impractical. In this study, we used carbon dioxide/graphite as the model system to explore the effects of finite dimensions on the description of experimental data of Terlain, A.; Larher, Y. Surf. Sci. 1983, 125 (1), 304-311, especially for temperatures below the bulk triple point temperature. With the appropriate choice of graphene size, we derived the 2D triple point and 2D critical point temperatures of the monolayer, and most importantly, for temperatures below the 2D critical point temperature, the adsorption mechanism for the formation of the monolayer is due to the interplay between the boundary growth process and the vacancy filling. The extent of this interplay is found to depend on the fractional coverage of the surface.

Stabilized SQP Methods in Hilbert Spaces

Based on techniques by (S.J. Wright 1998) for finite-dimensional optimization, we investigate a stabilized sequential quadratic programming method for nonlinear optimization problems in infinite-dimensional Hilbert spaces. The method is shown to achieve fast local convergence even in the absence of a constraint qualification, generalizing the results obtained by (S.J. Wright 1998 and W.W. Hager 1999) in finite dimensions to this broader setting.

Decidability of topological quasi-Boolean algebras

A sequent calculus S for the variety tqBa of all topological quasi-Boolean algebras is established. Using a construction of syntactic finite algebraic model, the finite model property of S is shown, and thus the decidability of S is obtained. We also introduce two non-distributive variants of topological quasi-Boolean algebras. For the variety TDM 5 of all topological De Morgan lattices with the axiom 5, we establish a sequent calculus S 5 and prove that the cut elimination holds for it. Consequently the decidability of S 5 is established. Furthermore, this proof-theoretic method is applied to some subvarieties of TDM 5 .

Theoretical Investigation of Transport Properties of X-doped (X = Cl, P, N) Graphene Quantum Dots Layer Adsorbed with Ammonia Molecule Using Non-Equilibrium Green’s Function

This study investigates the various transport properties, including Density of States (DOS), Transmission Coefficient, Current-Voltage Characteristics (I-V), and HOMO-LUMO energy levels, of X-doped (X = Cl, P, N) graphene quantum dot (GQD) layers with adsorbed ammonia molecules using density functional theory and non-equilibrium Green's function techniques. Our findings revealed the profound influence of different doping and adsorption scenarios on the transport properties of GQD layers. Specifically, chlorine doping leads to notably stronger resonance peaks, resulting in enhanced conductivity of the GQD layer. This effect is less pronounced for P-doped and N-doped GQDs, which exhibit minimal changes in conductance capability. Importantly, we observed a prominent interaction between ammonia molecules and chlorine-doped GQD layers. The HOMO and LUMO energy levels exhibit double degeneracy, significantly impacting edge passivation and the finite dimensions of GQDs, consequently reducing the energy gap. As a result, chlorine-doped GQD layers with adsorbed ammonia molecules exhibit increased energy levels and stronger current characteristics compared to P-GQDs and N-GQDs. HOMO and LUMO are doubly degenerated which has a clear effect on edge passivation as well as the finite size of GQDs and reduces energy gap. Therefore, more energy level and stronger current is available for chlorine doped graphene quantum dots layer with adsorbed ammonia molecule than P-GQDs and N-GQDs. Our theoretical finding highlighted the significant features of edge passivation, doping effect and adsorption of ammonia molecule onto graphene quantum dots layer. Our theoretical analysis highlighted key features encompassing edge passivation, doping effects, and ammonia molecule adsorption on GQD layers. These insights not only develop our fundamental understanding of these systems but also hold promise for novel applications that harness their distinct electronic properties.

Network Design and Control: Shape and Topology Optimization for the Turnpike Property for the Wave Equation

The optimal control problems for the wave equation are considered on networks. The turnpike property is shown for the state equation, the adjoint state equation as well as the optimal cost. The shape and topology optimization is performed for the network with the shape functional given by the optimality system of the control problem. The set of admissible shapes for the network is compact in finite dimensions, thus the use of turnpike property is straightforward. The topology optimization is analysed for an example of nucleation of a small cycle at the internal node of network. The topological derivative of the cost is introduced and evaluated in the framework of domain decomposition technique. Numerical examples are provided.

NUMERICAL STUDIES OF THE DISTRIBUTION CAPACITY AND DEFORMABILITY OF THE SPATIAL MODEL OF THE SOIL BASE IN THE FORM OF A LINEAR-DEFORMED LAYER

The article analyses the existing approaches to modelling the interaction between a structure and a soil foundation, which consider the joint deformation of the soil and the structure. The “base-foundation-structure” models can be created in one-dimensional, two-dimensional, or three-dimensional space. Each of these models has its own set of boundary conditions and calculation methodology The advantages and disadvantages of each model, during application in engineering calculations, are presented. The purpose of research is to substantiate the methodology for assigning the geometric parameters of a three-dimensional model of a soil foundation, represented as a linearly deformed layer of finite resolution, for adequate modelling of interaction in the "base- foundation-structure" system. A finite-element model of the interaction between the soil base and the slab foundation was built using the modern SCAD software package. The modelling was performed in three dimensions. The soil base is represented by volumetric finite elements with constant deformation characteristics. The foundation is modelled by plate finite elements In context of this research, the slab model of the foundation was assumed to be rigid to neglect stress redistribution in the above-ground part of the building. Based on the analysis of modern approaches to the assignment of geometric parameters to the model of the soil base represented by a continuous linearly deformed layer with finite overall dimensions, which is created in a three-dimensional problem statement, it was shown that today there is no single approach to modelling such a “base-foundation-structure” system. Numerical studies of the effect of rigid horizontal constraints in the plan on the stress-strain state of a uniformly loaded rigid foundation interacting with a linearly deformed layer (compressible thickness) of finite distribution capacity were carried out using the SCAD program. Based on the analysis of the results of numerical calculations for a three-dimensional problem, the minimum allowable sizes in terms of the model of a linearly deformed layer of finite distribution capacity, which considers the distribution of compressive stresses along the depth at an angle of α = 25º to the vertical from the edges of the loaded foundation, are substantiated. At the same time, the overall size of the model in the plan according to the distribution angle α = 25º has practically no effect on the average settlement and maximum moment forces of the foundation compared to the angle α = 45º. Keywords: slab foundation, soil foundation, linear-deformed model, distribution angle, stress-strain state.

Bethe M-layer construction on the Ising model

In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in disordered models, some important finite dimensional second-order phase transitions are qualitatively different or absent in the corresponding fully connected model: in such cases the standard expansion fails. Recently, a new method, the M-layer one, has been introduced that performs an expansion around a different soluble mean field model: the Bethe lattice one. This new method has been already used to compute the upper critical dimension DU of different disordered systems such as the Random Field Ising model or the Spin glass model with field. If then one wants to go beyond and construct an expansion around DU to understand how critical quantities get renormalized, the actual computation of all the numerical factors is needed. This next step has still not been performed, being technically more involved. In this paper we perform this computation for the ferromagnetic Ising model without quenched disorder, in finite dimensions: we show that, at one-loop order inside the M-layer approach, we recover the continuum quartic field theory and we are able to identify the coupling constant g and the other parameters of the theory, as a function of macroscopic and microscopic details of the model such as the lattice spacing, the physical lattice dimension and the temperature. This is a fundamental step that will help in applying in the future the same techniques to more complicated systems, for which the standard field theoretical approach is impracticable.

Exponential convergence of the weighted Birkhoff average

In this paper, we consider the polynomial and exponential convergence rates of the weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to the quasiperiodic and almost periodic dynamical systems respectively, under certain balance between the nonresonant condition and the decay rate of the Fourier coefficients. Diophantine rotations with finite and infinite dimensions are provided as examples. For the first time, we prove the universality of exponential convergence and arbitrary polynomial convergence in the quasiperiodic case and almost periodic case under analyticity respectively.

Finiteness properties of locally defined groups

Let X be a set and let S be an inverse semigroup of partial bijections of X . Thus, an element of S is a bijection between two subsets of X , and the set S is required to be closed under the operations of taking inverses and compositions of functions. We define \Gamma_{S} to be the set of self-bijections of X in which each \gamma \in \Gamma_{S} is expressible as a union of finitely many members of S . This set is a group with respect to composition. The groups \Gamma_{S} form a class containing numerous widely studied groups, such as Thompson’s group V , the Nekrashevych–Röver groups, Houghton’s groups, and the Brin–Thompson groups nV , among many others. We offer a unified construction of geometric models for \Gamma_{S} and a general framework for studying the finiteness properties of these groups.

Tunable Phonon Polariton Hybridization in a Van der Waals Hetero-Bicrystal.

Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero-bicrystals composed of molybdenum oxide (MoO3) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO3-hBN hetero-bicrystals self-assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along "forbidden" directions are also investigated in microscale bicrystals, which arise from the finite in-plane dimension of the synthesized MoO3 micro-ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub-wavelength mid-infrared light-matter interactions.

Quasi-pure resolutions and some lower bounds of Hilbert coefficients of Cohen-Macaulay modules

Let (A,m) be a Noetherian local ring and let M be a finitely generated Cohen Macaulay A module. Let G(A)=⨁n≥0mn/mn+1 be the associated graded ring of A and G(M)=⨁n≥0mnM/mn+1M be the associated graded module of M. If A is regular and if G(M) has a quasi-pure resolution then we show that G(M) is Cohen-Macaulay. If A is Gorenstein and G(A) is Cohen-Macaulay and if M has finite projective dimension then we give lower bounds on e0(M) and e1(M). Finally let A=Q/(f1,…,fc) be a strict complete intersection with ord(fi)=s for all i, where Q is a regular local ring. Let M be an Cohen-Macaulay module with complexity cxA(M)=r<c. We give lower bounds on e0(M) and e1(M).

Nuclear Dimension of Subhomogeneous Twisted Groupoid C*-algebras and Dynamic Asymptotic Dimension

Abstract We characterize subhomogeneity for twisted étale groupoid $\text{C}^{*}$-algebras and obtain an upper bound on their nuclear dimension. As an application, we remove the principality assumption in recent results on upper bounds on the nuclear dimension of a twisted étale groupoid $\text{C}^{*}$-algebra in terms of the dynamic asymptotic dimension of the groupoid and the covering dimension of its unit space. As a non-principal example, we show that the dynamic asymptotic dimension of any minimal (not necessarily free) action of the infinite dihedral group $D_{\infty }$ on an infinite compact Hausdorff space $X$ is always one. So if we further assume that $X$ is second-countable and has finite covering dimension, then $C(X)\rtimes _{r} D_{\infty }$ has finite nuclear dimension and is classifiable by its Elliott invariant.

Dynamic Simulation of a Molten Salt-Steam Superheater for Load-Following Applications

Abstract The growing use of intermittent renewables in electrical grids increasingly motivates load-following operations as a crucial capability of dispatchable power plants. However, frequent load variations in steam generation equipment can cause premature heat exchanger failure. This paper simulates the dynamic behavior of a high pressure, U-tube/U-shell, salt-to-steam superheater typically found in tower-type concentrating solar power subcritical Rankine cycles. Results focus on responses during load-following and inlet temperature changes. The proposed model is a finite volume method, and thermodynamic and heat transfer properties of both fluids are allowed to vary spatially and temporally. Several flow ramping schemes are investigated, including proportionally equal ramps and proportionally dissimilar ramping, where one fluid reaches its mass flow setpoint faster than the other. Results indicate that salt outlet temperature overshoot can occur if ramp rates are of sufficiently high magnitude, and that U-bend metal temperature rate of change can be approximately 2.5× that observed at either outlet. If proportionally-matched ramping is not possible, ramping steam more slowly than the salt is preferred over the alternative, as cold side and U-bend temperature responses are better regulated. Additionally, mass flow rate and inlet temperature changes are shown to elicit unique responses in the tube bundle metal.

Weakly compact sets in Orlicz–Bochner sequence spaces

AbstractIn this work, we give three kinds of criteria for weak sets in Orlicz–Bochner sequence spaces without constraints, conditions posited in each criterion are necessary and sufficient. As an application, we give criteria for weak sets in Orlicz sequence spaces. Well‐known conclusions are exhibited once more, such as Schur's theorem, Banach–Alaoglu's theorem, and the boundedly compact principle of finite dimension space. The results obtained show that the weak compactness may not be extrapolated straightforwardly from to , for example, .