Elliptic Deformation Research Articles

Elliptic deformation of the Gaiotto-Rapčák corner VOA and the associated partially symmetric polynoimals

We construct the elliptic Miura transformation and use it to obtain the expression of the currents of elliptic corner VOA. We subsequently prove a novel combinatorial formula that is essential for deriving the quadratic relations of the currents. In addition, we give a conjecture that relates the correlation function of the currents of elliptic corner VOA to a certain family of partially symmetric polynomials. The elliptic Macdonald polynomials, constructed recently by Awata-Kanno- Mironov-Morozov-Zenkevich, and Fukuda-Ohkubo-Shiraishi, can be obtained as a particular case of this family.

Geometry of the spectral parameter and renormalisation of integrable sigma-models

In the past few years, the unifying frameworks of 4-dimensional Chern-Simons theory and affine Gaudin models have allowed for the systematic construction of a large family of integrable σ-models. These models depend on the data of a Riemann surface C (here of genus 0 or 1) and of a meromorphic 1-form ω on C, which encodes the geometry of their spectral parameter and the analytic structure of their Lax connection. The main subject of this paper is the renormalisation of these theories and in particular two conjectures describing their 1-loop RG-flow in terms of the 1-form ω. These conjectures were put forward in [1] and [2] and were proven in a variety of cases. After extending the proposal of [1] to the elliptic setup (with C of genus 1), we establish the equivalence of these two conjectures and discuss some of their applications. Moreover, we check their veracity on an explicit example, namely an integrable elliptic deformation of the Principal Chiral Model on \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\ ext{SL}}}_{\\mathbb{R}}\\left(N\\right)$$\\end{document}.

An elliptic integrable deformation of the Principal Chiral Model

We introduce a new elliptic integrable σ-model in the form of a two-parameter deformation of the Principal Chiral Model on the group SLℝ(N), generalising a construction of Cherednik for N = 2 (up to reality conditions). We exhibit the Lax connection and R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{R} $$\\end{document}-matrix of this theory, which depend meromorphically on a spectral parameter valued in the torus. Furthermore, we explain the origin of this model from an equivariant semi-holomorphic 4-dimensional Chern-Simons theory on the torus. This approach opens the way for the construction of a large class of elliptic integrable σ-models, with the deformed Principal Chiral Model as the simplest example.

Elliptic deformations of the AdS3 × S3 × T4 string

Abstract With the aim of investigating the existence of an integrable elliptic deformation of strings on AdS3 × S3 × T4, we compute the tree-level worldsheet S-matrix of the elliptically-deformed bosonic sigma model on AdS3 × S3 in uniform light-cone gauge. The resulting tree-level S-matrix is compatible with the integrability of the model and has interesting features, including a hidden U(1) symmetry not manifest in the Lagrangian. We find that it cannot be embedded in the known exact integrable R-matrices describing deformations of the undeformed AdS3 × S3 × T4 light-cone gauge S-matrix including fermions. Therefore, we construct embeddings of the deformed 6-d metric in type II supergravity with constant dilaton and homogeneous fluxes. The simplicity of these solutions suggests they are promising candidates to lead to an integrable string sigma model including fermions.

Compressor airfoil optimization method driven by data-mechanism integration based on evolutionary multi-tasking algorithm

To address the challenge of the "curse of dimensionality" in aerodynamic design optimization of compressors, this study introduces an innovative optimization technique suitable for compressor airfoil design. This technique, rooted in a hybrid mechanism-data-driven approach, seamlessly integrates a hierarchical parameterization method, based on elliptic topological deformation, into a multitasking evolutionary algorithm framework. This integration deviates from the conventional approach of treating parameterization methods and optimization algorithms as distinct elements. The proposed method positions airfoil parameterization as its core, constructing two tasks within the optimization algorithm. It leverages the critical influence of the parameterization method on the aerodynamic performance landscape of the airfoils and the intrinsic qualities of the hierarchical parameterization method in the design space. The multitasking evolutionary optimization framework facilitates effective information exchange between tasks, significantly boosting optimization efficiency. In comparison to standard data-driven multitasking evolutionary algorithms, the proposed method achieves superior optimized solutions with merely 11 × D aerodynamic performance evaluations, where D denotes the number of design variables.

Modulations of the work function and morphology of a single MoS2 nanotube by charge injection.

Both the miniaturization of transistor components and the ongoing investigation of material systems with potential for quantum information processing have significantly increased current interest of researchers in semiconducting inorganic nanotubes. Here we report on an additional outstanding aspect of these nanostructures, namely the intrinsic coupling of electronic and mechanical properties. We observe electronic and morphology changes in a single MoS2 nanotube, exposed to charge injections by means of an atomic-force-microscopy tip. An elliptic deformation of the nanotube and helical twisting of the nanotube are visible, consistent with the reverse piezoelectric effect. Work-function changes are found to be dependent on the polarity of the injected carriers. An unexpected long-term persistence of the shape deformations is observed and explained with accumulation of structural defects and the resultant strain, which could cause a memory-like charge confinement and a long lasting modulation of the work function.

A range three elliptic deformation of the Hubbard model

In this paper we present a new integrable deformation of the Hubbard model. Our deformation gives rise to a range 3 interaction term in the Hamiltonian which does not preserve spin or particle number. This is the first non-trivial medium range deformation of the Hubbard model that is integrable. Our model can be mapped to a new integrable nearest-neighbour model via a duality transformation. The resulting nearest-neighbour model also breaks spin conservation. We compute the RR-matrices for our models, and find that there is a very unusual dependence on the spectral parameters in terms of the elliptic amplitude.

Performance of parallel double pipelines under non-uniform seismic excitation

This paper investigates the structural safety of parallel double-buried pipelines under non-uniform seismic excitation considering the soil-pipeline interaction. A three-dimensional nonlinear numerical model has been established to study the effects of seismic wave propagation and ground motion intensity, as well as the pipeline internal pressure and spacing between the pipelines on their structural safety. The dynamic response of the parallel double buried pipelines was evaluated in terms of the acceleration amplification, settlement of ground surface, and strain, displacement, and elliptical deformation of the pipeline. The results demonstrate that the seismic response of buried pipelines under non-uniform excitation has obvious nonlinear characteristics, especially when the loading intensity is high. It is found that the internal pressure has virtually no effect on the site acceleration response, but it amplifies the settlement of the ground surface. Meawhile, it inhibits the elliptic deformation of the pipeline. Furthermore, the variation of the elliptic deformation of parallel buried pipelines is found to be the same for different pipeline spacings considered in this study. On the other hand, the pipelines spacing has a significant influence on their seismic response as the interaction between the two pipelines gradually decreases with the increase in the spacing.

Discreteness of cell–surface contacts affects spatio-temporal dynamics, adhesion, and proliferation of mouse embryonic stem cells

The self-renewal and lineage-specific differentiation of stem cells are regulated by interactions with their microenvironments, called stem cell niche. Stem cells receive both biochemical and biophysical cues from their niche, which leads to the activation of signaling pathways, resulting in the modulation of gene expressions to guide their fate. Most of previous studies are focused on the effect of substrate stiffness using hydrogels with different Young’s moduli, and information is lacking on the effect of the discreteness of cell–substrate contacts on stem cells. Using mouse pluripotent, embryonic stem cells (mESCs) as the model system for early development, we quantitatively investigated the migration, dynamic deformation, and adhesion of mESCs on sparse and dense gelatin nanofibers deposited on glass surfaces, with a continuous layer of gelatin coated on glass substrates as the control. After confirming the maintenance of pluripotency on all the surfaces throughout the experiments, the centroid trajectories were monitored using timelapse imaging. The mean square displacement analysis indicated that both the diffusion coefficient and exponent were largest on sparse nanofibers, while the diffusion coefficient of mESCs on dense nanofibers was comparable to that on the control. Moreover, power spectral analysis of the shape deformation in the Fourier mode indicated that mESCs predominantly underwent elliptic deformation (mode 2), with the largest energy dissipation on sparse nanofibers. These data suggest that mESCs can deform and move on sparse nanofibers owing to the discrete cell–surface contact points. Intriguingly, using a self-developed technique based on laser-induced shock waves, a distinctly larger critical pressure was required to detach cells from nanofibers than from continuous gelatin. This finding suggests that the continuous but weak cell-substrate contacts suppress the deformation-driven mESC migration. As one of the key biological functions of stem cells, the proliferation rate of mESCs on these surfaces was determined. Although the observed difference was not statistically significant, the highest proliferation rate was observed on nanofibers, suggesting that the discreteness of cell–surface contacts can be used to regulate not only spatio-temporal dynamics but also the biological function of pluripotent stem cells.

Investigations on the intrinsic and template-dependent transformations of AlPO4-11 molecular sieve under high pressure

In this study, aluminophosphate molecular sieve AlPO4-11, with one-dimensional elliptical channels, was investigated under high pressure in non-penetrating silicone oil by X-ray powder diffraction, infrared spectroscopy and theoretical simulation, focusing on its intrinsic and template-modified mechanical behaviors. Two distinct compressible regimes were observed for both the calcined and as-synthesized AlPO4-11 frameworks before pressure-induced amorphization (PIA). The channel cross-section in the calcined AlPO4-11 framework showed an obvious increase in the ellipticity during this process. The framework structure began to lose crystallinity at approximately 2–3 GPa and underwent significant amorphization at 6.6 GPa. PIA was mainly induced via the destruction of the constructed species along the periodic crystallographic planes which are parallel to the channel axis. The bulk moduli showed that this empty framework was rather soft in these regimes. For the as-synthesized AlPO4-11 framework, the mechanical stability of the channels was markedly improved by the template molecules. A different elliptic deformation of the cross-section with a reduced contractility in the minor axis direction was presented. Discontinuous volume evolution occurs at 3–4 GPa and significant amorphization was postponed to 13.7 GPa. The as-synthesized AlPO4-11 was stiffer than calcined AlPO4-11 and showed a soft to hard transformation due to the strengthened host-guest interaction upon compression. Moreover, infrared spectra indirectly confirmed the structural collapses by detecting the vibrational characteristics of the embedded template molecules. The present results provided a comparative and basic knowledge of the intrinsic and extrinsic stability, compressibility, channel deformation and collapse of the AlPO4-11 framework under high pressure. This study emphasized the importance of guest molecules in modifying the mechanical behaviors of zeolites and resisting framework collapse.

Integrable deformations of AdS/CFT

In this paper we study in detail the deformations introduced in [1] of the integrable structures of the AdS2,3 integrable models. We do this by embedding the corresponding scattering matrices into the most general solutions of the Yang-Baxter equation. We show that there are several non-trivial embeddings and corresponding deformations. We work out crossing symmetry for these models and study their symmetry algebras and representations. In particular, we identify a new elliptic deformation of the AdS3× S3× M4 string sigma model.

Aharonov-Bohm oscillations in phosphorene quantum rings: Mass anisotropy compensation by confinement potential

We consider the Aharonov-Bohm (AB) effect on a confined electron ground state in a quantum ring defined electrostatically within the phosphorene monolayer. The strong anisotropy of effective masses in phosphorene quenches ground-state oscillations for a circular ring because of interrupted persistent current circulation around the ring. An elliptic deformation of the confinement potential can compensate for the anisotropy of the effective masses and produce ground-state parity transformations with the AB periodicity. Moreover, a specific ratio of the semiaxes is determined for which the spectrum becomes identical to that of a circular quantum ring and an isotropic effective mass. We identify a generalized angular momentum operator which commutes with the continuum Hamiltonian for the chosen ratio of the semiaxes that closes the avoided crossings of energy levels for states of the same parity and spin. Ground-state oscillations for the two-electron ground state are also discussed.

Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T overline{mathrm{T}} deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models mathcal{M} 2,2n+3.

Quasi-Hopf twist and elliptic Nekrasov factor

We investigate the quasi-Hopf twist of the quantum toroidal algebra of {mathfrak{gl}}_1 as an elliptic deformation. Under the quasi-Hopf twist the underlying algebra remains the same, but the coproduct is deformed, where the twist parameter p is identified as the elliptic modulus. Computing the quasi-Hopf twist of the R matrix, we uncover the relation to the elliptic lift of the Nekrasov factor for instanton counting of the quiver gauge theories on ℝ4× T2. The same R matrix also appears in the commutation relation of the intertwiners, which implies an elliptic quantum KZ equation for the trace of intertwiners. We also show that it allows a solution which is factorized into the elliptic Nekrasov factors and the triple elliptic gamma function.

Simulation of optical properties of ellipsoidal monocapillary X-ray optics with inner-surface imperfections

Ellipsoidal monocapillary x-ray optics are used as condenser lenses in full-field transmission x-ray microscopy. The numerical aperture (NA) of the ellipsoidal monocapillary is designed to match that of the x-ray zone plate objective. In practice, monocapillaries have inner-surface errors that lead to mismatches between the monocapillary and the zone plate. In this study, mathematical models of monocapillaries with elliptic cross-section deformation and centreline straightness errors were developed, respectively. Furthermore, the optical properties of these monocapillaries were simulated based on a ray-tracing method. The simulation provides a qualitative picture of the NA and illumination angle distributions of the ellipsoidal monocapillary with inner-surface errors, and it is useful for predicting the inner-surface imperfections from the x-ray ring behind the monocapillary.

Towards elliptic deformation of q,t-matrix models

As a necessary step in construction of elliptic matrix models, which preserve the superintegrability property <char>∼char, we suggest an elliptic deformation of the peculiar loci pkΔn, which play an important role in precise formulation of this property. The suggestion is to define the pkΔn-loci as elliptic functions with the right asymptotics at τ→i∞. If this hypothesis is correct, one can move to substituting the Schur and Macdonald functions in the role of characters by the elliptic GNS and study their behavior at the deformed topological and Δ loci.

The Mechanical Fingerprint of Circulating Tumor Cells (CTCs) in Breast Cancer Patients.

Simple SummaryDetection of circulating tumor cells (CTCs) in the blood of cancer patients is a challenging issue, since they adapt to the biochemical and physical landscape of the bloodstream. We approached the issue of CTC identification on a biophysical level. For the first time, we recorded the mechanical deformation profiles of potential CTCs, which were isolated from the blood of breast cancer patients, at the force regime of the deforming blood flow. Mechanical fingerprints of CTCs were significantly different from healthy white blood cells. We used machine learning to further evaluate the differences and identify discrimination criteria. Our results suggest that mechanical characterization of CTCs at low forces is a promising path towards CTC detection.Circulating tumor cells (CTCs) are a potential predictive surrogate marker for disease monitoring. Due to the sparse knowledge about their phenotype and its changes during cancer progression and treatment response, CTC isolation remains challenging. Here we focused on the mechanical characterization of circulating non-hematopoietic cells from breast cancer patients to evaluate its utility for CTC detection. For proof of premise, we used healthy peripheral blood mononuclear cells (PBMCs), human MDA-MB 231 breast cancer cells and human HL-60 leukemia cells to create a CTC model system. For translational experiments CD45 negative cells—possible CTCs—were isolated from blood samples of patients with mamma carcinoma. Cells were mechanically characterized in the optical stretcher (OS). Active and passive cell mechanical data were related with physiological descriptors by a random forest (RF) classifier to identify cell type specific properties. Cancer cells were well distinguishable from PBMC in cell line tests. Analysis of clinical samples revealed that in PBMC the elliptic deformation was significantly increased compared to non-hematopoietic cells. Interestingly, non-hematopoietic cells showed significantly higher shape restoration. Based on Kelvin–Voigt modeling, the RF algorithm revealed that elliptic deformation and shape restoration were crucial parameters and that the OS discriminated non-hematopoietic cells from PBMC with an accuracy of 0.69, a sensitivity of 0.74, and specificity of 0.63. The CD45 negative cell population in the blood of breast cancer patients is mechanically distinguishable from healthy PBMC. Together with cell morphology, the mechanical fingerprint might be an appropriate tool for marker-free CTC detection.

Investigation on strain characteristic of buried natural gas pipeline under longitudinal landslide debris flow

In order to ensure the safe operation of buried natural gas pipeline (BNGP) under landslide debris flow (LDF), a model is established to investigate the strain characteristic of BNGP. The influence of longitudinal LDF morphology is analyzed for the elliptic deformation rate, tensile and compression strain of BNGP. The results show that the influence area of LDF is about 5 m from the upstream and downstream position of active area, respectively. The peak value of elliptic deformation rate is mainly impacted by the thickness and length of LDF, and will increase linearly with that. The maximum value of axial strains will also increase linearly with length, thickness and breadth of LDF. It will decrease with the angle of mountain slope and depth of BNGP. The fracture failure of BNGP may be occurred at the active area of LDF and upstream position of that. But the local yield or fold failure of BNGP will be occurred at the active area of LDF and downstream position of that. At the same time, a method is proposed to estimate the maximum value of elliptic deformation rate and axial strains of BNGP under longitudinal LDF. The deviations between the prediction results and simulation data are less than ±10%.

Scattering equations in AdS: scalar correlators in arbitrary dimensions

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

Two-phase piecewise homogeneous plane deformations of a fibre-reinforced neo-Hookean material with application to fibre kinking and splitting

Two-phase piecewise homogeneous plane deformations are examined in respect of a neo-Hookean matrix material reinforced with embedded aligned fibres characterized by a single stiffness parameter. The deformations are interpreted in terms of fibre kinking and fibre splitting. Previous work has shown that such a transversely isotropic material can lose ellipticity if the reinforcing stiffness is sufficiently large and the fibre direction is sufficiently compressed. In particular, it was shown that the associated failure modes are characterised by the emergence of weak surfaces of discontinuity that are normal to the fibre direction (the onset of fibre kinking) or parallel to the fibre direction (the onset of fibre splitting). Here, the analysis of strong surfaces of discontinuity, developing from weak ones, is studied. The considered model can give rise to piecewise smooth plane deformations separated by a plane stationary surface of discontinuity, interpreted as either kinking or splitting. Attention is restricted to (plane) deformations in which, on one side of the surface of discontinuity, the load axis is aligned with the fibre axis. Then the fibre stretch on this side of the discontinuity is a natural load parameter. The ellipticity status of the two-phase piecewise homogeneous plane deformations is shown to span all four possible ellipticity/non-ellipticity permutations. If both deformation states are elliptic, then a suitable intermediate deformation is shown to be non-elliptic. Moreover, it is shown that the mechanism is dissipative, and maximally dissipative quasi-static failure motion is examined in respect of both kinking and splitting. It follows that, firstly, surfaces of discontinuity perpendicular to the fibre direction, associated with fibre kinking, are nucleated followed by surfaces of discontinuity parallel to the fibre direction, associated with fibre splitting. With respect to kinking, such maximally dissipative kinks nucleate only in compression as weak surfaces of discontinuity, with the subsequent motion converting non-elliptic deformation to elliptic deformation.