Continuum Thermodynamic Modeling and Simulation of Electromagnetic Metal Forming

The purpose of this work is the formulation and application of a continuum field approach to the phenomenological modeling of a class of engineering materials which can be dynamically formed using strong magnetic fields. This is done in the framework of a thermodynamic, internal-variable-based formulation in which the deformation, temperature and magnetic fields are in general coupled. As is well-known, this coupling takes the form of the Lorentz force as an additional supply of momentum, and the electromotive power as an additional supply of energy, in the material. The constitutive formulation is based as usual on the exploitation of the dissipation principle, here for the case of generally anisotropic, elastoviscoplastic material behaviour. In particular, the general results so obtained are applied in particular to the case of small strain and large rotation. As shown here, in this special case, the electromagnetic field relations become independent of the deformation field. As such, they can be solved independently and used as input for the solution of the thermomechanical field relations. Application of this reduced formulation for small strain to the simulation of the electromagnetic forming of an aluminum tube shows the importance of accounting for inertial effects and rate-dependence in the modeling

Augmentation varieties and disk potentials II

This is the second in a sequence of papers in which we construct Chekanov-Eliashberg algebras for Legendrians in circle-fibered contact manifolds and study the associated augmentation varieties. In this part, we first define the Chekanov-Eliashberg algebra and its Legendrian contact homology. For a tame Lagrangian cobordism between Legendrians, we define a chain map between their Chekanov-Eliashberg algebras.Comment: 52 pages; The original manuscript arXiv:2310.17821v1 was split into three parts: this being part I

Augmentation varieties and disk potentials III

This is the third in a series of papers in which we construct Chekanov-Eliashberg algebras for Legendrians in circle-fibered contact manifolds and study the associated augmentation varieties. In this part, we prove that for connected Legendrian covers of monotone Lagrangian tori, the augmentation variety is equal to the image of the zero level set of the disk potential, as suggested by Dimitroglou-Rizell-Golovko. In particular, we show that Legendrian lifts of Vianna's exotic tori are not Legendrian isotopic. Using related ideas, we show that the Legendrian lift of the Clifford torus admits no exact fillings, extending results of Dimitroglou-Rizell and Treumann-Zaslow in dimension two. We consider certain disconnected Legendrians, and show, similar to another suggestion of Aganagic-Ekholm-Ng-Vafa that the components of the augmentation variety correspond to certain partitions and each component is defined by a (not necessarily exact) Lagrangian filling.Comment: 42 pages; The original manuscript arXiv:2310.17821v1 was split into three parts: this being part II

Augmentation varieties and disk potentials

We elaborate on a suggestion of Aganagic-Ekholm-Ng-Vafa, that in order for Lagrangian fillings such as the Harvey-Lawson filling to define augmentations of Chekanov-Eliashberg differential graded algebras, one should count configurations of holomorphic disks connected by gradient trajectories. We propose a definition of the Chekanov-Eliashberg dga in higher dimensions which includes as generators both Reeb chords and the space of chains on the Legendrian, similar to the definition of immersed Lagrangian Floer theory whose generators are chains on the Lagrangian as well as self-intersection points. We prove that for connected Legendrian covers of monotone Lagrangian tori, the augmentation variety in this model is equal to the image of the zero level set of the disk potential, as suggested by Dimitroglou-Rizell-Golovko. In particular, we show that Legendrian lifts of Vianna's exotic tori are not Legendrian isotopic, as conjectured in Dimitroglou-Rizell-Golovko. Using related ideas, we show that the Legendrian lift of the Clifford torus admits no exact fillings, extending the results of Dimitroglou-Rizell and Treumann-Zaslow in dimension two. We consider certain disconnected Legendrians, and show, similar to another suggestion of Aganagic-Ekholm-Ng-Vafa, that the components of the augmentation variety correspond to certain partitions and each component is defined by a (not necessarily exact) Lagrangian filling. An adaptation of the theory of holomorphic quilts shows that the cobordism maps associated to bounding chains are independent of all choices up to chain homotopy.Comment: 157 page

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published pape

Axion Emission from Red Giants and White Dwarfs

Using thermal field theory methods, we recalculate axion emission from dense plasmas. We study in particular the Primakoff and the bremsstrahlung processes. The Primakoff rate is significantly suppressed at high densities, when the electrons become relativistic. However, the bound on the axion-photon coupling, $G<10^{-10}$ GeV, is unaffected, as it is constrained by the evolution of HB stars, which have low densities. In contradistinction, the same relativistic effects enhance the bremsstrahlung processes. From the red giants and white dwarfs evolution, we obtain a conservative bound on the axion-electron coupling, $g_{ae} < 2\times 10^{-13}$.Comment: 17 pp, 3 PS figures, CERN-TH-7044/9

Kinetics of Polymerisation of Furfuryl Alcohol in Aqueous Solution

SUMMARY: Kinetic information on the polymerisation of furfuryl alcohol catalysed by Clark-Lubs&apos; aqueous buffer in the pH range of 1.G2.2 has been derived from the rate of increase ofcolour intensity measured with a photoelectric colorimeter. The polymerisation reaction is found to be of zero order, with the activation energy increasing exponentially with pH. The time required to reach the extent of reaction at which a resin layer separates out from the aqueous solution decreases with increasing temperature but increases with increasing pH. An exponential expression relating the time for phase separation with temperature and pH has been derived. ZUSAMMENFASSUNG: Einblicke in die Kinetik der Polymerisation von Furfurylalkohol, die durch eine wlDrige Pufferlosung nach Clark-Lubs im pH-Bereich von 1,0 bis 2.2 ausgelost wurde, konnten ausder Geschwindigkeit der Zunahme der Farbintensitat, die mit einem photoelektrischen Kolorimeter gemessen wurde, gewonnen werden. Die Reaktionsordnung der Polymerisation wurde zu null bestimmt; die Aktivierungsenergie nimmt mit dem pH-Wert exponentiell zu. Die Zeitspanne bis zu einem Urnsat4 bei dem sich eine Polymerphasc von der wPl3rigen Phase abtrennt, nimmt mit steigender Temperatur ab, steigt jedoch mit zunehmendem pH-Wert. Ein exponentieller Zusammenhang mischen der Zeitspanne bis zur Phasentrennung und der Temperatur sowie dem pH-Wert wurde abgeleitet

Static and dynamical quantum correlations in phases of an alternating field XY model

We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a non-monotonic behavior of entanglement with respect to temperature in the anti-ferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information theoretic measures can be both ergodic as well as non-ergodic, depending on the system parameters.Comment: 20 Pages, 13 Figures, 2 Tables, Published versio

Reducing Computational Complexity of Quantum Correlations

We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having non-positive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states.Comment: 19 pages, 14 figures, 3 table