Topic

# Type (model theory)

About: Type (model theory) is a research topic. Over the lifetime, 38949 publications have been published within this topic receiving 670564 citations.

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TL;DR: Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.

Abstract: A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_{a}|$ is found to scale as $({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\simeq}0.45$.

5,729 citations

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TL;DR: A form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators, and finds that all late-3d-transition-metal monoxides, as well as the parent compounds of the high-${\mathit{T}$ compounds, are large-gap magnetic insulators of the charge-transfer type.

Abstract: We propose a form for the exchange-correlation potential in local-density band theory, appropriate for Mott insulators The idea is to use the ``constrained-local-density-approximation'' Hubbard parameter U as the quantity relating the single-particle potentials to the magnetic- (and orbital-) order parameters Our energy functional is that of the local-density approximation plus the mean-field approximation to the remaining part of the U term We argue that such a method should make sense, if one accepts the Hubbard model and the success of constrained-local-density-approximation parameter calculations Using this ab initio scheme, we find that all late-3d-transition-metal monoxides, as well as the parent compounds of the high-${\mathit{T}}_{\mathit{c}}$ compounds, are large-gap magnetic insulators of the charge-transfer type Further, the method predicts that ${\mathrm{LiNiO}}_{2}$ is a low-spin ferromagnet and NiS a local-moment p-type metal The present version of the scheme fails for the early-3d-transition-metal monoxides and for the late 3d transition metals

4,697 citations

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TL;DR: In this paper, a superconductive solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian, and the pions of finite mass are found as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangians which otherwise possesses a certain type of the ∆-ensuremath{gamma{5}$ invariance.

Abstract: Continuing the program developed in a previous paper, a "superconductive" solution describing the proton-neutron doublet is obtained from a nonlinear spinor field Lagrangian. We find the pions of finite mass as nucleon-antinucleon bound states by introducing a small bare mass into the Lagrangian which otherwise possesses a certain type of the ${\ensuremath{\gamma}}_{5}$ invariance. In addition, heavier mesons and two-nucleon bound states are obtained in the same approximation. On the basis of numerical mass relations, it is suggested that the bare nucleon field is similar to the electron-neutrino field, and further speculations are made concerning the complete description of the baryons and leptons.

3,684 citations

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Kyoto University

^{1}TL;DR: In this article, the tetragonal to orthorhombic ferroelastic phase transition between rutile- and CaCl-type phonon modes at high pressures is studied using first-principles calculations and the Landau free-energy expansion.

Abstract: The tetragonal to orthorhombic ferroelastic phase transition between rutile- and ${\text{CaCl}}_{2}$-type ${\text{SiO}}_{2}$ at high pressures is studied using first-principles calculations and the Landau free-energy expansion. The phase transition is systematically investigated in terms of characteristic phonon modes with ${\text{B}}_{1g}$ and ${\text{A}}_{g}$ symmetries, shear moduli, transverse-acoustic mode, rotation angle of the ${\text{SiO}}_{6}$ octahedra, spontaneous symmetry-breaking and volume strains, and enthalpy. The results show that these physical behaviors at the transition are well described using the Landau free-energy expansion parametrized by the first-principles calculations.

3,503 citations

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TL;DR: In this paper, the authors developed a stochastic transport model for the transient photocurrent, which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface.

Abstract: Measurements of the transient photocurrent $I(t)$ in an increasing number of inorganic and organic amorphous materials display anomalous transport properties. The long tail of $I(t)$ indicates a dispersion of carrier transit times. However, the shape invariance of $I(t)$ to electric field and sample thickness (designated as universality for the classes of materials here considered) is incompatible with traditional concepts of statistical spreading, i.e., a Gaussian carrier packet. We have developed a stochastic transport model for $I(t)$ which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface. The time dependence of the random walk is governed by hopping time distribution $\ensuremath{\Psi}(t)$. A packet, generated with a $\ensuremath{\Psi}(t)$ characteristic of hopping in a disordered system [e.g., $\ensuremath{\Psi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}(1+\ensuremath{\alpha})}$, $0l\ensuremath{\alpha}l1$], is shown to propagate with a number of anomalous non-Gaussian properties. The calculated $I(t)$ associated with this packet not only obeys the property of universality but can account quantitatively for a large variety of experiments. The new method of data analysis advanced by the theory allows one to directly extract the transit time even for a featureless current trace. In particular, we shall analyze both an inorganic ($a\ensuremath{-}{\mathrm{As}}_{2}{\mathrm{Se}}_{3}$) and an organic (trinitrofluorenone-polyvinylcarbazole) system. Our function $\ensuremath{\Psi}(t)$ is related to a first-principles calculation. It is to be emphasized that these $\ensuremath{\Psi}(t)$'s characterize a realization of a non-Markoffian transport process. Moreover, the theory shows the limitations of the concept of a mobility in this dispersive type of transport.

2,489 citations