Non-linear autonomous systems of differential equations and Carleman linearization procedure

AbstractThe non-linear autonomous of differential equations ẋi=∑jaijxj+∑j,kbijkxjxk(ẋi=dxi/dt, i, j, k= 1,2,…n) which plays an important role in chemical kinetics and other fields of physics (turbulence and plasma physics) is investigated using the Carleman linearization procedure

Calorimetric Investigation of CeRu2Ge2 up to 8 GPa

We have developed a calorimeter able to give a qualitative picture of the specific heat of a sample under high pressure up to approximately 10 GPa. The principle of ac-calorimetry was adapted to the conditions in a high pressure clamp. The performance of this technique was successfully tested with the measurement of the specific heat of CeRu2Ge2 in the temperature range 1.5 K<T<12 K. The phase diagram of its magnetic phases is consistent with previous transport measurements.Comment: 5 pages, 4 figure

Magnetic phase transitions in the two-dimensional frustrated quantum antiferromagnet Cs2CuCl4

We report magnetization and specific heat measurements in the 2D frustrated spin-1/2 Heisenberg antiferromagnet Cs2CuCl4 at temperatures down to 0.05 K and high magnetic fields up to 11.5 T applied along a, b and c-axes. The low-field susceptibility chi (T) M/B shows a broad maximum around 2.8 K characteristic of short-range antiferromagnetic correlations and the overall temperature dependence is well described by high temperature series expansion calculations for the partially frustrated triangular lattice with J=4.46 K and J'/J=1/3. At much lower temperatures (< 0.4 K) and in in-plane field (along b and c-axes) several new intermediate-field ordered phases are observed in-between the low-field incommensurate spiral and the high-field saturated ferromagnetic state. The ground state energy extracted from the magnetization curve shows strong zero-point quantum fluctuations in the ground state at low and intermediate fields

The Josephson critical current in a long mesoscopic S-N-S junction

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/\epsilon_{c}$ and $k_{B}T/\epsilon_{c}$ where $\epsilon_{c}$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.Comment: 5 pages, 4 figures, slighly modified version, publishe

Dephasing of a superconducting flux qubit

In order to gain a better understanding of the origin of decoherence in superconducting flux qubits, we have measured the magnetic field dependence of the characteristic energy relaxation time ($T_1$) and echo phase relaxation time ($T_2^{\rm echo}$) near the optimal operating point of a flux qubit. We have measured $T_2^{\rm echo}$ by means of the phase cycling method. At the optimal point, we found the relation $T_2^{\rm echo}\approx 2T_1$. This means that the echo decay time is {\it limited by the energy relaxation} ($T_1$ process). Moving away from the optimal point, we observe a {\it linear} increase of the phase relaxation rate ($1/T_{2}^{\rm echo}$) with the applied external magnetic flux. This behavior can be well explained by the influence of magnetic flux noise with a $1/f$ spectrum on the qubit

Representation of Equilibrium Conditions for the Carbon Monoxide - Carbon Dioxide - Steel System

Proper conditioning of atmospheres for carburizing, for heat treating, and for carrying out other high temperature metallurgical processes depends in general on control of each system with regard to its equilibrium conditions. In connection with steel processing, numerous investigations have been made to determine equilibrium conditions for the most common gas-steel reactions. One such reaction that has been studied extensively takes place when certain mixtures of carbon monoxide and carbon dioxide come in contact with ordinary carbon steel at elevated temperatures. The purpose of this paper is to review some of the methods that have been used to represent equilibrium for this gas-steel reaction and to present a condensed but more comprehensive treatment of equilibrium for the system

Strain enhancement of superconductivity in CePd2Si2 under pressure

We report resistivity and calorimetric measurements on two single crystals of CePd2Si2 pressurized up to 7.4 GPa. A weak uniaxial stress induced in the pressure cell demonstrates the sensitivity of the physics to anisotropy. Stress applied along the c-axis extends the whole phase diagram to higher pressures and enhances the superconducting phase emerging around the magnetic instability, with a 40% increase of the maximum superconducting temperature, Tc, and a doubled pressure range. Calorimetric measurements demonstrate the bulk nature of the superconductivity.Comment: 4 pages, 4 figure