In many sliding systems consisting of solid object on a solid substrate under dry condition, the friction force does not depend on the apparent contact area and is proportional to the loading force. This behaviour is called Amontons' law and indicates that the friction coefficient, or the ratio of the friction force to the loading force, is constant. Here, however, using numerical and analytical methods, we show that Amontons' law breaks down systematically under certain conditions for an elastic object experiencing a friction force that locally obeys Amontons' law. The macroscopic static friction coefficient, which corresponds to the onset of bulk sliding of the object, decreases as pressure or system length increases. This decrease results from precursor slips before the onset of bulk sliding, and is consistent with the results of certain previous experiments. The mechanisms for these behaviours are clarified. These results will provide new insight into controlling friction.

Micelacking both Kv3.1 and both Kv3.3 K+ channel alleles display severe motor deficits such as tremor, myoclonus, and ataxic gait. Micelacking one to three alleles at the Kv3.1 and Kv3.3 loci exhibit in an allele dose-dependent manner a modest degree of ataxia. Cerebellar granule cells coexpress Kv3.1 and Kv3.3 K+ channels and are therefore candidate neurons that might be involved in these behavioral deficits. Hence, we investigated the synaptic mechanisms of transmission in the parallel fiber-Purkinje cell system. Action potentials of parallel fibers were broader in mice lacking both Kv3.1 and both Kv3.3 alleles and in mice lacking both Kv3.1 and a single Kv3.3 allele compared with those of wild-type mice. The transmission of high-frequency trains of action potentials was only impaired at 200 Hz but not at 100 Hz in mice lacking both Kv3.1 and Kv3.3 genes. However, paired-pulse facilitation (PPF) at parallel fiber-Purkinje cell synapses was dramatically reduced in a gene dose-dependent manner in mice lacking Kv3.1 or Kv3.3 alleles. Normal PPF could be restored by reducing the extracellular Ca2+ concentration indicating that increased activity-dependent presynaptic Ca2+ influx, at least in part caused the altered PPF in mutant mice. Induction of metabotropic glutamate receptor-mediated EPSCs was facilitated, whereas longterm depression was not impaired but rather facilitated in Kv3.1/Kv3.3 double-knockout mice. These results demonstrate the importance of Kv3 potassium channels in regulating the dynamics of synaptic transmission at the parallel fiber-Purkinje cell synapse and suggest a correlation between short-term plasticity at the parallel fiber-Purkinje cell synapse and motor performance.

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The Néel and the singlet RVB orders of the t-J model in a 2D square lattice are studied in the slave-boson mean-field approximation. It is shown that the Néel order parameter takes the maximum value at the finite temperature and disappear at the lower temperature for a certain range of doping. It is also shown that the Néel and the singlet RVB orders coexist at low temperature.This suggests the possibility of the coexistence of the Néel and the superconducting orders. I. INTRODUCTIONIn order to make clear the mechanism of high-T c superconductivity in cuprates, it is indispensable to understand the whole phase diagram on the temperature-doping plane. Recent theoretical studies by the slave-boson mean-field theory based on the t-J model show the validities of the method and the model for high-T c cuprates [ 1− 4]. These studies, however, do not take into account the Néel order explicitly. A few works based on the same theoretical scheme study the Néel order [ 5,6]. In ref. 5 the Néel order and the singlet RVB order parameters are considered, but the bond order parameters are not treated in the self-consistent way. In ref. 6 the Néel order and the bond order parameters of spinon and holon are included. It is shown that there is a phase transition between itinerant and localized antiferromagnetism in the Néel state. But the singlet RVB order is not studied there.