On the decay of Burgers turbulence

This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small wavenumbers $k$ and falling off quickly at large wavenumbers. In physical space, at sufficiently large distances, there is an ``outer region'', where the velocity correlation function preserves exactly its initial form (a power law) when $n$ is not an even integer. When $1<n<2$ the spectrum, at long times, has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, stemming from this outer region, in which the initial conditions are essentially frozen; second, a $k^2$ region at intermediate wavenumbers, related to a self-similarly evolving ``inner region'' in physical space and, finally, the usual $k^{-2}$ region, associated to the shocks. The switching from the $|k|^n$ to the $k^2$ region occurs around a wave number $k_s(t) \propto t^{-1/[2(2-n)]}$, while the switching from $k^2$ to $k^{-2}$ occurs around $k_L(t)\propto t^{-1/2}$ (ignoring logarithmic corrections in both instances). The key element in the derivation of the results is an extension of the Kida (1979) log-corrected $1/t$ law for the energy decay when $n=2$ to the case of arbitrary integer or non-integer $n>1$. A systematic derivation is given in which both the leading term and estimates of higher order corrections can be obtained. High-resolution numerical simulations are presented which support our findings.Comment: In LaTeX with 11 PostScript figures. 56 pages. One figure contributed by Alain Noullez (Observatoire de Nice, France

Upaya Peningkatan Kemampuan Menyebutkan Simbol-Simbol Huruf Melalui Permainan Kartu Huruf Pada Kelompok A Tk Aisyiyah I Pandeyan Ngemplak Boyolali Tahun Ajaran 2011 / 2012

Penelitian ini merupakan penelitian tindakan kelas. Penelitian ini bertujuan untuk mengetahui peningkatan kemampuan menyebutkan simbol-simbol huruf melalui permainan kartu huruf. Subyek dalam penelitian ini adalah anak didik kelompok A TK Aisyiyah I Pandeyan berjumlah 25 anak . Penelitian ini bersifat kolaboratif antara peneliti, guru kelas dan kepala sekolah. Data yang dikumpulkan melalui observasi yaitu dengan lembar observasi, catatan lapangan, dan dokumentasi. Data dianalisis secara deskriptif kualitatif model alur. Hasil ini menunjukkan bahwa tingkat kemampuan menyebutkan simbol-simbol huruf di kelompok A TK Aisyiyah I Pandeyan. Sebelum dilakukan penelitian tindakan kelas yaitu anak dapat menyebutkan simbol-simbol huruf sebesar 43%. Setelah dilakukan tindakan yang disepakati yaitu dengan menggunakan metode permainan kartu huruf pada proses pembelajaran meningkatkan kemampuan menyebutkan simbol-simbol huruf diperoleh hasil yaitu Siklus I menjadi 64%, Siklus II meningkat menjadi 73% dan Siklus III meningkat menjadi 84%. Hasil penelitian ini sudah memenuhi indikator pencapaian. Berdasarkan hasil penelitian tindakan kelas tersebut maka hipotesis tindakan yang menyatakan “Diduga dengan menggunakan permainan kartu huruf dapat meningkatkan kemampuan menyebutkan simbol-simbol huruf pada TK Aisyiyah I Pandeyan tahun pelajaran 2011/2012” terbukti dan dapat diterima kebenarannya

Soliton Magnetization Dynamics in Spin-Orbit Coupled Bose-Einstein Condensates

Ring-trapped Bose-Einstein condensates subject to spin-orbit coupling support localized dark soliton excitations that show periodic density dynamics in real space. In addition to the density feature, solitons also carry a localized pseudo-spin magnetization that exhibits a rich and tunable dynamics. Analytic results for Rashba-type spin-orbit coupling and spin-invariant interactions predict a conserved magnitude and precessional motion for the soliton magnetization that allows for the simulation of spin-related geometric phases recently seen in electronic transport measurements.Comment: 3 figures, 5 page

Effect of Poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include

High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

A numerical method of high precision is used to calculate the energy eigenvalues and eigenfunctions for a symmetric double-well potential. The method is based on enclosing the system within two infinite walls with a large but finite separation and developing a power series solution for the Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with those obtained on the basis of the Zinn-Justin conjecture and found to be in an excellent agreement.Comment: Substantial changes including the title and the content of the paper 8 pages, 2 figures, 3 table

Pair-wise decoherence in coupled spin qubit networks

Experiments involving phase coherent dynamics of networks of spins, such as echo experiments, will only work if decoherence can be suppressed. We show here, by analyzing the particular example of a crystalline network of Fe8 molecules, that most decoherence typically comes from pairwise interactions (particularly dipolar interactions) between the spins, which cause `correlated errors'. However at very low T these are strongly suppressed. These results have important implications for the design of quantum information processing systems using electronic spins.Comment: 4 pages, 4 figures. Final PRL versio