On first-order expressibility of satisfiability in submodels

Let $\kappa,\lambda$ be regular cardinals, $\lambda\le\kappa$, let $\varphi$ be a sentence of the language $\mathcal L_{\kappa,\lambda}$ in a given signature, and let $\vartheta(\varphi)$ express the fact that $\varphi$ holds in a submodel, i.e., any model $\mathfrak A$ in the signature satisfies $\vartheta(\varphi)$ if and only if some submodel $\mathfrak B$ of $\mathfrak A$ satisfies $\varphi$. It was shown in [1] that, whenever $\varphi$ is in $\mathcal L_{\kappa,\omega}$ in the signature having less than $\kappa$ functional symbols (and arbitrarily many predicate symbols), then $\vartheta(\varphi)$ is equivalent to a monadic existential sentence in the second-order language $\mathcal L^{2}_{\kappa,\omega}$, and that for any signature having at least one binary predicate symbol there exists $\varphi$ in $\mathcal L_{\omega,\omega}$ such that $\vartheta(\varphi)$ is not equivalent to any (first-order) sentence in $\mathcal L_{\infty,\omega}$. Nevertheless, in certain cases $\vartheta(\varphi)$ are first-order expressible. In this note, we provide several (syntactical and semantical) characterizations of the case when $\vartheta(\varphi)$ is in $\mathcal L_{\kappa,\kappa}$ and $\kappa$ is $\omega$ or a certain large cardinal

The 25 October 2010 Mentawai tsunami earthquake (M_w 7.8) and the tsunami hazard presented by shallow megathrust ruptures

The 25 October 2010 Mentawai, Indonesia earthquake (M_w 7.8) ruptured the shallow portion of the subduction zone seaward of the Mentawai islands, off-shore of Sumatra, generating 3 to 9 m tsunami run-up along southwestern coasts of the Pagai Islands that took at least 431 lives. Analyses of teleseismic P, SH and Rayleigh waves for finite-fault source rupture characteristics indicate ∼90 s rupture duration with a low rupture velocity of ∼1.5 km/s on the 10° dipping megathrust, with total slip of 2–4 m over an ∼100 km long source region. The seismic moment-scaled energy release is 1.4 × 10^(−6), lower than 2.4 × 10^(−6) found for the 17 July 2006 Java tsunami earthquake (M_w 7.8). The Mentawai event ruptured up-dip of the slip region of the 12 September 2007 Kepulauan earthquake (M_w 7.9), and together with the 4 January 1907 (M 7.6) tsunami earthquake located seaward of Simeulue Island to the northwest along the arc, demonstrates the significant tsunami generation potential for shallow megathrust ruptures in regions up-dip of great underthrusting events in Indonesia and elsewhere

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

This essay examines the philosophical significance of $\Omega$-logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of $\Omega$-logical validity can then be countenanced within a coalgebraic logic, and $\Omega$-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of $\Omega$-logical validity correspond to those of second-order logical consequence, $\Omega$-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets

Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice

We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. Among several formulations, we study models by Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem is absent in both models and that they converge to the identical continuum limit without fine tuning. We provide a simple explanation why previous works by other authors, which claim an existence of the sign problem, do not capture the continuum physics.Comment: 27 pages, 24 figures; v2: comments and references added; v3: figures on U(1) mass independence and references added, to appear in JHE

The chiral and flavour projection of Dirac-Kahler fermions in the geometric discretization

It is shown that an exact chiral symmetry can be described for Dirac-Kahler fermions using the two complexes of the geometric discretization. This principle is extended to describe exact flavour projection and it is shown that this necessitates the introduction of a new operator and two new structures of complex. To describe simultaneous chiral and flavour projection, eight complexes are needed in all and it is shown that projection leaves a single flavour of chiral field on each.Comment: v2: 17 pages, Latex. 5 images eps. Added references, reformatted and clarification of some point

State of stress before and after the 1994 Northridge Earthquake

The state of tectonic stress in the epicentral area of the 17 January 1994, Northridge earthquake (Mw 6.7) is investigated by applying a stress inversion method to P-wave polarity data from earthquakes in Northridge from July 1981 to January 1994 and from the Northridge aftershocks during January 1994 to December 1995. A 3-D crustal model is used to trace the rays taking off from the hypocenter, which reduced the effects of large structural heterogeneities on the determination of the stress tensor. We found significant temporal changes of stress orientations induced by the Northridge earthquake. The principal pressure (P) axis is oriented N32°E from 1981 to June 1992, and N30°E from 28 June 1992 to 16 January 1994, suggesting that the stress field in Northridge was not affected by the 1992 Landers earthquake. During two weeks following the Northridge mainshock, the P-axis is oriented N13°E, which is a significant (17°) change from that before the earthquake (N30°E). Between February 1994 and August 1995 the P-axis orientation changes from N18°E to N26°E, and finally ends up at N34° by the end of 1995, which is close to that before the Northridge earthquake. These results suggest that the stresses rotated coseismically, then rotated more slowly back to their original orientation. The aftershocks caused by the mainshock changed the stress distribution in the crust, which showed up as a regional stress change. The stress recovery appears to have completed within two years after the mainshock, which is very short compared to the time scale of the earthquake cycle

Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states

A Hubbard model with a N_d-fold degenerate single-particle ground state has ferromagnetic ground states if the number of electrons is less or equal to N_d. It is shown rigorously that the local stability of ferromagnetism in such a model implies global stability: The model has only ferromagnetic ground states, if there are no single spin-flip ground states. If the number of electrons is equal to N_d, it is well known that the ferromagnetic ground state is unique if and only if the single-particle density matrix is irreducible. We present a simplified proof for this result.Comment: accepted for publication in J. Phys.

Radiated Energy and the Physics of Earthquake Faulting

On the third day of a recent AGU Chapman Conference, held in Portland, Maine, near the Two Lights fault zones and the Fort Foster brittle zone, conference participants spent the gray June day scrambling over rocky ledges above the crashing surf along the coast of the Atlantic Ocean. With field trip leader Mark Swanson, who with his students has studied the area in detail over the past 20 years, participants examined evidence of ancient earthquakes from about 300 million years ago when these rocks were 8 to 10 kilometers deep. This evidence included pseudotachylytes—glass generated by heating during fault slip at midcrustal depths

Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra

The lattice superalgebra of the link approach is shown to satisfy a Hopf algebraic supersymmetry where the difference operator is introduced as a momentum operator. The breakdown of the Leibniz rule for the lattice difference operator is accommodated as a coproduct operation of (quasi)triangular Hopf algebra and the associated field theory is consistently defined as a braided quantum field theory. Algebraic formulation of path integral is perturbatively defined and Ward-Takahashi identity can be derived on the lattice. The claimed inconsistency of the link approach leading to the ordering ambiguity for a product of fields is solved by introducing an almost trivial braiding structure corresponding to the triangular structure of the Hopf algebraic superalgebra. This could be seen as a generalization of spin and statistics relation on the lattice. From the consistency of this braiding structure of fields a grading nature for the momentum operator is required.Comment: 45 page