Strict Deformation Research Articles

Characteristics of deformation and defect of shield tunnel in coastal structured soil in China

Shield tunnel is a type of linear underground structure assembled by lining segments, characterized with long joint, weak stiffness, and strict deformation control requirement. The situation of the long-term deformation and defect of the shield tunnel in soft ground in coastal area of China is severe, mainly attributed to the tunneling-induced ground consolidation, frozen cross passage, groundwater pumping, cyclic train load, and nearby construction. Shield tunnel is buried in ground, and the above factors could result in underlying ground settlement, overlying ground loading/unloading, and at-side ground unloading. As a result, the tunnel could suffer from different types of structural deformation and defect. Based upon the aforementioned different reasons, this study investigates the characteristics of the tunnel deformation and defect corresponding to the different types of ground stress change and deformation. It is found that tunneling-induced ground consolidation, frozen cross passage, groundwater pumping, and cyclic train load mainly contribute to the longitudinal differential settlement but negligible transverse convergence, associated with water leakages at circumferential joints. In comparison, surface surcharge and at-side unloading not only cause significant longitudinal differential deformation but also increase transverse lining internal forces, resulting in water leakages at circumferential joints, longitudinal lining concrete cracks and water leakages. Finally, nearby construction could strongly disturb the ground and cause the generation of excess pore-water pressure, making the shield tunnel deformation develops continuously after the nearby construction is completed.

Classical limits of Hilbert bimodules as symplectic dual pairs

Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic structures of the relevant types of models. Previously, it has been shown that one can functorially associate certain symplectic dual pairs to Hilbert bimodules through strict deformation quantization. We show that, in the inverse direction, strict deformation quantization also allows one to functorially take the classical limit of a Hilbert bimodule to reconstruct a symplectic dual pair.

Function theory off the complexified unit circle: Fréchet space structure and automorphisms

Motivated by recent work on strict deformation quantization of the unit disk and the Riemann sphere, we study the Fréchet space structure of the set of holomorphic functions on the complement \(\Omega:=\{(z,w)\in \hat{\mathbb{C}}^2\colon z\cdot w\not=1\}\) of the complexified unit circle \(\{(z,w) \in \hat{\mathbb{C}}^2 \colon z\cdot w=1\}\). We also characterize the subgroup of all biholomorphic automorphisms of \(\Omega\) which leave the canonical Laplacian on \(\Omega\) invariant.

Strict Deformation Quantization and Local Spin Interactions

We define a strict deformation quantization which is compatible with any Hamiltonian with local spin interaction (e.g. the Heisenberg Hamiltonian) for a spin chain. This is a generalization of previous results known for mean-field theories. The main idea is to study the asymptotic properties of a suitably defined algebra of sequences invariant under the group generated by a cyclic permutation. Our point of view is similar to the one adopted by Landsman, Moretti and van de Ven (Rev Math Phys 32(10):2050031, 2020, https://doi.org/10.1142/S0129055X20500312), who considered a strict deformation quantization for the case of mean-field theories. However, the methods for a local spin interaction are considerably more involved, due to the presence of a strictly smaller symmetry group.

Strict Quantization of Polynomial Poisson Structures

We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on {mathbb {R}}^d, generalizing known results for constant and linear Poisson structures to polynomial Poisson structures of arbitrary degree. We give several examples of nonlinear Poisson structures and construct explicit formal star products whose deformation parameter can be evaluated to any real value of hbar , giving strict quantizations on the space of analytic functions on {mathbb {R}}^d with infinite radius of convergence. We also address further questions such as continuity of the classical limit hbar rightarrow 0, compatibility with ^*-involutions, and the existence of positive linear functionals. The latter can be used to realize the strict quantizations as ^*-algebras of operators on a pre-Hilbert space which we demonstrate in a concrete example.

Experimental research and application of old combined bridge barriers with non-standard sections

To improve the protective performance of old combined bridge barriers with non-standard sections, this article has improved the guardrail scheme. The newly improved guardrail is evaluated by finite element simulation, yield line theory calculation, and a crash test to see whether it reaches class SA protection. The results show that the blocking, redirecting, and buffering functions of the improved scheme meet the Standard for Safety Performance Evaluation of Highway Barriers (JTG B05-01-2013), and its protection class reaches class SA. The bridge barrier with strict deformation control cannot be evaluated by the yield line theory calculation alone. Thus, the evaluation should be assisted with finite element simulation and a crash test. The improved scheme has been successfully applied to engineering practice. With simple construction, safety, and reliability, the scheme effectively reduces engineering costs and improves the protective performance of old combined bridge barriers with non-standard sections.

Numerical Method for the Deformation Calculation of the Shallow Buried Tunnel Caused by the Excavation of Overlying Soil Based on Soil Rebounding Characteristics

In view of strict deformation control standards, it is important to calculate the shallow tunnel deformation caused by the unloading of overburdened soil for analyzing tunnel structure safety. Due to the obvious nonlinear characteristics and the significantly smaller rebound deformation of soil under unloading conditions, previous numerical calculation methods need to be improved and adapted to the soil deformation characteristics under unloading. Based on the above background, cyclic loading and unloading tests were carried out to study the deformation characteristics of soil under different loading levels, stress history, and unloading levels. Secondly, a unified modulus calculation model was established, especially for the unloading modulus, which considers the unloading stress history and current unloading stress level, and can provide the value of soil modulus in different states. The relationship between the unloading rebound modulus Esc and the rebound modulus Ec0 used in the numerical simulation was studied. Finally, a set of numerical calculation and analysis methods for shallow tunnel deformation caused by overlying soil excavation based on its rebounding characteristics is proposed. The rationality of the method is verified by two examples, and is applied to a practical project.

Research on Cumulative Deformation Characteristics of Subgrade Filling under Cyclic Train Loading

The smoothness of high-speed railway is extremely strict. As an important part of the high-speed railway foundation, the subgrade structure has strict deformation requirements. It is necessary to ensure that the subgrade structure does not have plastic cumulative deformation under the long-term cyclic load of the train, which is the most critical geodynamic problem in high-speed railway subgrade. This paper studied the cumulative deformation characteristics of subgrade filling under cyclic train loading through the cyclic triaxial test, three types of accumulative plastic deformation trends, and the value of critical volume shear strain was discussed, which would provide the theoretical support for the dynamic design of high-speed railway.

Strict deformation quantization of abelian lattice gauge fields

This paper shows how to construct classical and quantum field C*-algebras modeling a $U(1)^n$-gauge theory in any dimension using a novel approach to lattice gauge theory, while simultaneously constructing a strict deformation quantization between the respective field algebras. The construction starts with quantization maps defined on operator systems (instead of C*-algebras) associated to the lattices, in a way that quantization commutes with all lattice refinements, therefore giving rise to a quantization map on the continuum (meaning ultraviolet and infrared) limit. Although working with operator systems at the finite level, in the continuum limit we obtain genuine C*-algebras. We also prove that the C*-algebras (classical and quantum) are invariant under time evolutions related to the electric part of abelian Yang--Mills. Our classical and quantum systems at the finite level are essentially the ones of [van Nuland and Stienstra, 2020], which admit completely general dynamics, and we briefly discuss ways to extend this powerful result to the continuum limit. We also briefly discuss reduction, and how the current set-up should be generalized to the non-abelian case.

Numerical evaluation for cooling performance of a composite measure on expressway embankment with shady and sunny slopes in permafrost regions

As an efficient engineering measure for protecting permafrost from thawing, the composite measure composed of L-shaped two-phase closed thermosyphons (TPCTs), insulation board and crushed-rock revetments (CRs) is applied to the low-grade highway in the Qinghai-Tibet Plateau. However, it is uncertain whether this composite measure can be available for an expressway embankment with wide bituminous pavement and strict deformation requirement, and the deformation performance of the embankment with composite measure is the key factor controlling safe operation. In this study, a hydro-thermo-mechanical coupled model for the expressway embankment combined with the composite measure is developed, the working process and mechanism of L-shaped TPCTs, insulation board and CRs are analyzed, respectively, and the cooling and reinforcing effects of the composite measure for the embankment with shady and sunny slopes are evaluated. The numerical results show that: (1) The working process and mechanism of L-shaped TPCTs, insulation board and CRs are different. (2) The composite measure can not only prevent the permafrost degradation, but also relieve the asymmetric geotemperature and moisture distributions caused by shady-sunny slope effect. (3) The composite measure can significantly reduce the embankment deformation, reliably alleviate the deformation difference and reinforce the stability of the expressway embankment in permafrost regions.

Injective Tensor Products in Strict Deformation Quantization

The aim of this paper is twofold. Firstly we provide necessary and sufficient criteria for the existence of a strict deformation quantization of algebraic tensor products of Poisson algebras, and secondly we discuss the existence of products of KMS states. As an application, we discuss the correspondence between quantum and classical Hamiltonians in spin systems and we provide a relation between the resolvent of Schödinger operators for non-interacting many particle systems and quantization maps.

The classical limit of Schrödinger operators in the framework of Berezin quantization and spontaneous symmetry breaking as an emergent phenomenon

The algebraic properties of a strict deformation quantization are analyzed on the classical phase space [Formula: see text]. The corresponding quantization maps enable us to take the limit for [Formula: see text] of a suitable sequence of algebraic vector states induced by [Formula: see text]-dependent eigenvectors of several quantum models, in which the sequence converges to a probability measure on [Formula: see text], defining a classical algebraic state. The observables are here represented in terms of a Berezin quantization map which associates classical observables (functions on the phase space) to quantum observables (elements of [Formula: see text] algebras) parametrized by [Formula: see text]. The existence of this classical limit is in particular proved for ground states of a wide class of Schrödinger operators, where the classical limiting state is obtained in terms of a Haar integral. The support of the classical state (a probability measure on the phase space) is included in certain orbits in [Formula: see text] depending on the symmetry of the potential. In addition, since this [Formula: see text]-algebraic approach allows for both quantum and classical theories, it is highly suitable to study the theoretical concept of spontaneous symmetry breaking (SSB) as an emergent phenomenon when passing from the quantum realm to the classical world by switching off [Formula: see text]. To this end, a detailed mathematical description is outlined and it is shown how this algebraic approach sheds new light on spontaneous symmetry breaking in several physical models.

Is the classical limit “singular”?

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics.

Extensions of bundles of C*-algebras

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the [Formula: see text] limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the [Formula: see text] case) on the fiber C*-algebras.

The classical limit of mean-field quantum spin systems

The theory of strict deformation quantization of the two-sphere S2⊂R3 is used to prove the existence of the classical limit of mean-field quantum spin chains, whose ensuing Hamiltonians are denoted by HN, where N indicates the number of sites. Indeed, since the fibers A1/N=MN+1(C) and A0 = C(S2) form a continuous bundle of C*-algebras over the base space I={0}∪1/N*⊂[0,1], one can define a strict deformation quantization of A0 where quantization is specified by certain quantization maps Q1/N:Ã0→A1/N, with Ã0 being a dense Poisson subalgebra of A0. Given now a sequence of such HN, we show that under some assumptions, a sequence of eigenvectors ψN of HN has a classical limit in the sense that ω0(f) ≔ limN→∞⟨ψN, Q1/N(f)ψN⟩ exists as a state on A0 given by ω0(f)=1n∑i=1nf(Ωi), where n is some natural number. We give an application regarding spontaneous symmetry breaking, and moreover, we show that the spectrum of such a mean-field quantum spin system converges to the range of some polynomial in three real variables restricted to the sphere S2.

Practical prediction method on frost heave of soft clay in artificial ground freezing with field experiment

Artificial ground freezing (AGF) is a method of paramount importance for underground construction in soft soil area. There were numerous studies concerned on field observations and the theoretical formulations on frost heaves. However, the field observations and validity of the theoretical models from practical points were lack. This paper focused on a more accurate practical prediction method of frost heave by multilayer field experiments and segregation potential (SP) model, for a strict deformation requirement AGF project in a non-stopping airport during construction. Thus, a large-scale area (3.5 times than actual frozen curtain) field experiment of multilayered temperatures and displacements was conceived and developed, to evaluate the freezing effect and deformation characteristics. Temperature variations show that the additional freezing tubes at the tunnel opening can only achieve faster cooling rate initially but could not descend the final stable temperature, and so substantially increasing freezing tubes at the tunnel opening may not be best choice to keep excavation safe. Multilayered temperatures and displacements show that deformation of multi-layers is directly relevant to the position of frost front. A simplified frost heave prediction method using segregation potential concept is proposed based on field experimental data. The temperature gradient and frost front function have been calculated based on field monitoring results and served for the model computation. This prediction method was further validated by both other’s published and our field experimental data. 2–8% relative errors surrounding the axis of frozen curtain prove the applicability of this practical prediction model is much well. This paper provides valuable reference for urban tunneling under extreme conditions such as non-stopping airport or adjacent to existing structures.

Bulk-boundary asymptotic equivalence of two strict deformation quantizations

The existence of a strict deformation quantization of X_k=S(M_k({mathbb {C}})), the state space of the ktimes k matrices M_k({mathbb {C}}) which is canonically a compact Poisson manifold (with stratified boundary), has recently been proved by both authors and Landsman (Rev Math Phys 32:2050031, 2020. https://doi.org/10.1142/S0129055X20500312). In fact, since increasing tensor powers of the ktimes k matrices M_k({mathbb {C}}) are known to give rise to a continuous bundle of C^*-algebras over I={0}cup 1/mathbb {N}subset [0,1] with fibers A_{1/N}=M_k({mathbb {C}})^{otimes N} and A_0=C(X_k), we were able to define a strict deformation quantization of X_k à la Rieffel, specified by quantization maps Q_{1/N}:/ tilde{A}_0rightarrow A_{1/N}, with tilde{A}_0 a dense Poisson subalgebra of A_0. A similar result is known for the symplectic manifold S^2subset mathbb {R}^3, for which in this case the fibers A'_{1/N}=M_{N+1}(mathbb {C})cong B(text {Sym}^N(mathbb {C}^2)) and A_0'=C(S^2) form a continuous bundle of C^*-algebras over the same base space I, and where quantization is specified by (a priori different) quantization maps Q_{1/N}': tilde{A}_0' rightarrow A_{1/N}'. In this paper, we focus on the particular case X_2cong B^3 (i.e., the unit three-ball in mathbb {R}^3) and show that for any function fin tilde{A}_0 one has lim _{Nrightarrow infty }||(Q_{1/N}(f))|_{text {Sym}^N(mathbb {C}^2)}-Q_{1/N}'(f|_{_{S^2}})||_N=0, where text {Sym}^N(mathbb {C}^2) denotes the symmetric subspace of (mathbb {C}^2)^{N otimes }. Finally, we give an application regarding the (quantum) Curie–Weiss model.

Strict Deformation Quantization via Geometric Quantization in the Bieliavsky Plane

Using standard techniques from geometric quantization, we rederive the integral product of functions on ℝ2 (non-Euclidian) which was introduced by Pierre Bieliavsky as a contribution to the area of strict quantization. More specifically, by pairing the nontransverse real polarization on the pair groupoid ℝ2×ℝ¯2, we obtain the well-defined integral transform. Together with a convolution of functions, which is a natural deformation of the usual convolution of functions on the pair groupoid, this readily defines the Bieliavsky product on a subset of L2ℝ2.

Categorical perspective on quantization of Poisson algebra

We propose a generalization of quantization using a categorical approach. For a fixed Poisson algebra, quantization categories are defined as subcategories of the R-module category equipped with the structure of classical limits. We then construct the generalized quantization categories including matrix regularization, strict deformation quantization, prequantization, and Poisson enveloping algebra. It is shown that the categories of strict deformation quantization, prequantization, and matrix regularization with certain conditions are equivalent categories. On the other hand, the categories of Poisson enveloping algebra are not equivalent to the other categories.

Strictly Regulated Two-Dimensional Slippage in a Lamellar Single Crystal of 5-Fluorouracil

Slip deformability to multiple directions results in development of moldability and processability of solids as well as applications to solid lubricants. On the other hand, strict deformation in a ...