Stability of certain periodic solutions of a forced system with hysteresis

Many physical systems exhibit the phenomenon of nonlinear hysteresis when the amplitude of oscillation exceeds some small limit. It was shown that under certain conditions there are periodic motions of such a system with small forcing which are near the largest periodic motion of the corresponding unforced system. Conditions for the stability of these periodic motions are derived

Mechanical properties and the electronic structure of transition of metal alloys

This interdiscipline research program was undertaken in an effort to investigate the relationship between the mechanical strength of Mo based alloys with their electronic structure. Electronic properties of these alloys were examined through optical studies, and the classical solid solution strengthening mechanisms were considered, based on size and molecular differences to determine if these mechanisms could explain the hardness data

The magneto-optical Faraday effect in spin liquid candidates

We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac spinons. We give a semiquantitative estimate for the magnitude of the effect and find that it should be experimentally feasible to detect in both $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ and, if the spinons form a Fermi surface, Herbertsmithite. We also comment on the magneto-optical Kerr effect and show that the imaginary part of the Kerr angle may be measurable.Comment: 5 pages, 1 figur

Results and conjectures on simultaneous core partitions

An n-core partition is an integer partition whose Young diagram contains no hook lengths equal to n. We consider partitions that are simultaneously a-core and b-core for two relatively prime integers a and b. These are related to abacus diagrams and the combinatorics of the affine symmetric group (type A). We observe that self-conjugate simultaneous core partitions correspond to the combinatorics of type C, and use abacus diagrams to unite the discussion of these two sets of objects. In particular, we prove that (2n)- and (2mn+1)-core partitions correspond naturally to dominant alcoves in the m-Shi arrangement of type C_n, generalizing a result of Fishel--Vazirani for type A. We also introduce a major statistic on simultaneous n- and (n+1)-core partitions and on self-conjugate simultaneous (2n)- and (2n+1)-core partitions that yield q-analogues of the Coxeter-Catalan numbers of type A and type C. We present related conjectures and open questions on the average size of a simultaneous core partition, q-analogs of generalized Catalan numbers, and generalizations to other Coxeter groups. We also discuss connections with the cyclic sieving phenomenon and q,t-Catalan numbers.Comment: 17 pages; to appear in the European Journal of Combinatoric

Youth and the future: effective youth services for the year 2015

This report provides an understanding of the services required by young people in the year 2015, based on a thorough analysis of recent trends and expert projections of those trends. The report analyses key social and economic changes for young people in Australia over the past 10 to 20 years including movements in population, education, employment/unemployment and the labour market, incomes, family and household structure, health, and crime and justice

Proposal for a Topological Plasmon Spin Rectifier

We propose a device in which the spin-polarized AC plasmon mode in the surface state of a topological insulator nanostructure induces a static spin accumulation in a resonant, normal metal structure coupled to it. Using a finite-difference time-domain model, we simulate this spin-pump mechanism with drift, diffusion, relaxation, and precession in a magnetic field. This optically-driven system can serve as a DC "spin battery" for spintronic devices.Comment: Eq. 1 corrected; Figs 3 and 4 update