Replica theory of the rigidity of structural glasses

We present a first principle scheme to compute the rigidity, i. e. the shear-modulus of structural glasses at finite temperatures using the cloned liquid theory, which combines the replica theory and the liquid theory. With the aid of the replica method which enables disentanglement of thermal fluctuations in liquids into intra-state and inter-state fluctuations, we extract the rigidity of metastable amorphous solid states in the supercooled liquid and glass phases. The result can be understood intuitively without replicas. As a test case, we apply the scheme to the supercooled and glassy state of a binary mixture of soft-spheres. The result compares well with the shear-modulus obtained by a previous molecular dynamic simulation. The rigidity of metastable states is significantly reduced with respect to the instantaneous rigidity, namely the Born term, due to non-affine responses caused by displacements of particles inside cages at all temperatures down to T=0. It becomes nearly independent of temperature below the Kauzmann temperature T_K. At higher temperatures in the supercooled liquid state, the non-affine correction to the rigidity becomes stronger suggesting melting of the metastable solid state. Inter-state part of the static response implies jerky, intermittent stress-strain curves with static analogue of yielding at mesoscopic scales.Comment: 52 pages, 10 figure

Disorder-free spin glass transitions and jamming in exactly solvable mean-field models

We construct and analyze a family of $M$-component vectorial spin systems which exhibit glass transitions and jamming within supercooled paramagnetic states without quenched disorder. Our system is defined on lattices with connectivity $c=\alpha M$ and becomes exactly solvable in the limit of large number of components $M \to \infty$. We consider generic $p$-body interactions between the vectorial Ising/continuous spins with linear/non-linear potentials. The existence of self-generated randomness is demonstrated by showing that the random energy model is recovered from a $M$-component ferromagnetic $p$-spin Ising model in $M \to \infty$ and $p \to \infty$ limit. In our systems the quenched disorder, if present, and the self-generated disorder act additively. Our theory provides a unified mean-field theoretical framework for glass transitions of rotational degree of freedoms such as orientation of molecules in glass forming liquids, color angles in continuous coloring of graphs and vector spins of geometrically frustrated magnets. The rotational glass transitions accompany various types of replica symmetry breaking. In the case of repulsive hardcore interactions in the spin space, continuous the criticality of the jamming or SAT/UNSTAT transition becomes the same as that of hardspheres.Comment: 85 pages (9 figures) Revised and extended version submitted to SciPost Physics. (Analysis on anisotropic particles included in v2 will be presented in a separate publication.

Stable degenerations of Cohen-Macaulay modules

As a stable analogue of degenerations, we introduce the notion of stable degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient conditions for the stable degeneration. These conditions will be helpful to see when a Cohen-Macaulay module degenerates to another.Comment: 29 pages, to appear in Journal of Algebr

Low frequency seismogenic electromagnetic emissions as precursors to earthquakes and volcanic eruptions in Japan

A multipoint network was constructed in the Tokyo area for earthquake prediction using seismogenic electromagnetic emissions. The network consists of eight observation points within 50 km of each other.Each point has a digital direction-finding detector with two loop sensors tuned to 82 kHz. The output signals of the receivers are added into a digital vector composition circuit to obtain the direction angle of the source point,and this signal is telemetered to the central computer.To protect from false alarms caused by local man-made noise interference,the warning is announced only when there is a high cross-correlation between almost all detectors pointing to one small area. The mechanism of these earthquake precursors can be explained as electromagnetic emissions from the rocks around the focus when they are crushed completely by the distortion pressure. These emissions propagate along the fault plane as an EM surface wave mode and radiate from the slit antenna formed by the intersection of the fault plane and ground surface.In the last five years, we have detected impulsive noise bursts of seismogenic emissions at 82 kHz, 1.525 kHz, and 36 Hz using our multipoint detection network around the Tokyo region and Izu peninsula. This system has recorded EM signals prior to the following events: volcanic eruptions on November 15 and 2 1, 1986 at Mt. Mihara on Ohshima Island, and on July 12, 1989 in Itoh Bay in the Izu peninsula region, and also a minor earthquake on October 14, 1989 at Ohshima Island