Hierarchy of Chaotic Maps with an Invariant Measure

We give hierarchy of one-parameter family F(a,x) of maps of the interval [0,1] with an invariant measure. Using the measure, we calculate Kolmogorov-Sinai entropy, or equivalently Lyapunov characteristic exponent, of these maps analytically, where the results thus obtained have been approved with numerical simulation. In contrary to the usual one-parameter family of maps such as logistic and tent maps, these maps do not possess period doubling or period-n-tupling cascade bifurcation to chaos, but they have single fixed point attractor at certain parameter values, where they bifurcate directly to chaos without having period-n-tupling scenario exactly at these values of parameter whose Lyapunov characteristic exponent begins to be positive.Comment: 18 pages (Latex), 7 figure

Sign change of the Grueneisen parameter and magnetocaloric effect near quantum critical points

We consider the Grueneisen parameter and the magnetocaloric effect near a pressure and magnetic field controlled quantum critical point, respectively. Generically, the Grueneisen parameter (and the thermal expansion) displays a characteristic sign change close to the quantum-critical point signaling an accumulation of entropy. If the quantum critical point is the endpoint of a line of finite temperature phase transitions, T_c \propto (p_c-p)^Psi, then we obtain for p<p_c, (1) a characteristic increase \Gamma \sim T^{-1/(\nu z)} of the Grueneisen parameter Gamma for T>T_c, (2) a sign change in the Ginzburg regime of the classical transition, (3) possibly a peak at T_c, (4) a second increase Gamma \sim -T^{-1/(nu z)} below T_c for systems above the upper critical dimension and (5) a saturation of Gamma \propto 1/(p_c-p). We argue that due to the characteristic divergencies and sign changes the thermal expansion, the Grueneisen parameter and magnetocaloric effect are excellent tools to detect and identify putative quantum critical points.Comment: 10 pages, 7 figures; final version, only minor change

Voltage-current characteristic simulator Patent

Simulating voltage-current characteristic curves of solar cell panel with different operational parameter

A new mechanical structural damage feature index based on HHT

A new damage feature index is presented for the structural health monitoring based on Hilbert-Huang transform (HHT). The energy marginal spectrum of the dynamic signal is used to construct damage characteristic parameter, which can reflect the signal energy variation and benefit the structural damage detection. A sinusoidal wave with frequency change and a composite plate vibration experiment with pre-defined damage are designed to verify the effectiveness of characteristic parameter in damage detection. Results obtained from simulation and test show that the extracted non-model-based damage feature index is available and sensitive in damage detection of time-varying system.Peer Reviewe

The polynomial representation of the type An−1A_{n - 1} rational Cherednik algebra in characteristic p∣np \mid n

We study the polynomial representation of the rational Cherednik algebra of type $A_{n-1}$ with generic parameter in characteristic $p$ for $p \mid n$. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic $p$ analogues of existing characteristic $0$ results.Comment: 8 pages. v3: Streamlined proof of complete intersection property in Section 3; main results are unchange

Analytical formula of Free Electron Laser exponential gain for non-resonant electron beam

The FEL gain formulas for non-resonant case are studied. For the mono-energetic and non-resonant electron beam, the exact expression of the solution of the FEL characteristic cubic equation is obtained with a form much more simple than that in the literatures, and the gain length as the function of the detuning parameter is explicitly given, then the gain for different detuning parameter and from low to high can be easily calculated. A simplified approximation formula is also given for the exponential gain calculation in the non-resonant case. For the case of the electron beam with an energy spread, the solution of the characteristic cubic equation is given explicitly for rectangular energy distribution and Lorentz distribution, respectively. Moreover the explicit expression also can be used for the solution of the characteristic cubic equation including the impact of the space charge. The transition from the low gain to the high gain is analyzed. The variations of the gain bandwidth and of the detuning parameter for the maximum gain are demonstrated. The applicable ranges of the small signal gain formula and the exponential gain formula are analyzed.Comment: 9 pages, 8 figure