Synchronized cluster formation in coupled laser networks

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.     

Trapping of random walks on the line

Several features of the trapping of random walks on a one-dimensional lattice are analyzed. The results of this investigation are as follows: (1) The correction term to the known asymptotic form for the survival probability ton steps is O(( ₂n)^–1/3), where =–ln(1–c), andc is the trap concentration. (2) The short time form for the survival probability is found to be exp[–a(c)n ^1/2], wherea(c) is given in Eq. (21). (3) The mean-square displacement of a surviving random walker is found to go liken ^2/3for largen. (4) When the distribution of trap-free regions is changed so that very large regions are much rarer than for ideally random trap placement the asymptotic survival probability changes its dependence onn. One such model is studied.     

L''exactitude du rendement des machines agricoles

Precision of the working height, or depth, of earth-moving equipment and other farm machinery can have a marked effect on the quality of the operation. The main factors affecting a machine's performance in maintaining the correct working height are its geometric parameters and the soil surface upon which it operates. The soil surface profile is defined by the “mean slope”, by the “root-mean-square” (RMS) of the deviations from the mean slope, and by the wavelengths calculated by Fourier analysis. The shortest wavelength with an amplitude above 1 cm was used in this study to find the effect of the soil surface waves on the accuracy of farm machinery operations. The machine's geometric parameters affecting its accuracy are its wheelbase and the lengthwise location of the working point (above or under ground) in relation to the wheels. A computer simulation analysis showed that the minimum deviations from the required height are found at the wheels of the machine. The deviations increased at the middle of the machine's span and rose steeply outside the span. The shorter the wheel-span of the machine relative to the wavelengths, the smaller the deviations will be. Smoothed surfaces have longer wavelengths and smaller deviations and as a result, higher accuracy of the working height, or depth, of the machines working on them.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

Nuclear equation of state and compression modes

The nuclear matter (N = Z and no Coulomb interaction) incompressibility coefficient, K _nm , which is directly related to the curvature of the nuclear matter equation of state, is a very important physical quantity in the study of properties of nuclei, supernova collapse, neutron stars and heavy-ion collisions. We review the current status of K _nm and the experimental and theoretical methods used to determine the value of K _nm from the excitation crosssections σ(E) and the transition strength distributions S(E) of compression modes in nuclei. In particular, we will consider the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) and provide a simple explanation to the long standing problem of the conflicting results obtained for K _nm , deduced from experimental data on excitation cross sections for the ISGMR and data for the ISGDR.     

Properties of isolated DNA bases, base pairs and nucleosides examined by laser spectroscopy

The vibronic spectra of laser desorbed and jet cooled guanine (G) adenine (A), and cytosine (C) consist of bands from four, two and two major tautomers respectively, as revealed by UV-UV and IR-UV double resonance spectroscopy. The vibronic spectrum of adenine around 277 nm consists of weak nπ^* and strong ππ^* transitions, based on IR-UV and deuteration experiments. Precise ionization potentials of G and A were determined with 2-color, 2-photon ionization. We also measured vibronic and IR spectra of several base pairs. GC exhibits a HNH ^... OH/NH ^... N/C=O ^... HNH bonding similar to the Watson-Crick GC base pair but with C as enol tautomer. One GG isomer exhibits non-symmetric hydrogen bonding with HNH ^... N/NH ^... N/C=O ^... HNH interactions. A second observed GG isomer has a symmetrical hydrogen bond arrangement with C=O ^... NH/NH ^... O=C bonding. Two CC isomers were observed with symmetrical C=O ^... NH/NH ^... O=C bonding and nonsymmetrical C=O ^... HNH/NH ^... N interaction, respectively. Guanosine (Gs), 2-DeoxyGs und 3-DeoxyGs each exhibit only one isomer in the investigated wavelength range around 290 nm with a strong intramolecular sugar(5-OH) ^... enolguanine(3-N) hydrogen bond. Received 16 June 2002 / Received in final form 15 July 2002 Published online 13 September 2002     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.     

Anomalous transport in scale-free networks

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.     

A three dimensional dark focal spot uniformly surrounded by light

A new technique is proposed for generating a tight dark focal spot surrounded by uniform light intensity in all directions. It is based on a single focusing lens illuminated from one side, hence the alignment sensitivities associated with 4π methods are eliminated. Such a beam can be useful, e.g. as a dark atomic trap, and as the erase beam in three dimensional super-resolution fluorescence microscopy.