1,427 research outputs found
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
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,
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, .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' 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
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