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This article presents a theory of collisions of continua either solid or not. The basic idea which is developed is that the system made of distinct continua is deformable because their relative positions change. The collisions we ...
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This article presents a theory of collisions of continua either solid or not. The basic idea which is developed is that the system made of distinct continua is deformable because their relative positions change. The collisions we consider occur while the continua are evolving and the duration of the collisions is small compare to the duration of the whole motion. Thus they are assumed instantaneous. We do not focus on the fast and sophisticated phenomena which occur during collisions. We focus on summing up these phenomena in a coherent theory which gives the elements to pursue the description of the motion. This instantaneity assumption leaves large possibilities to engineers and scientists to develop numerous and useful predictive theories. The basis of the theory is illustrated with the collision of a point with an immobile obstacle. Then the theory is applied to collisions of solids, either rigid or deformable, then to collisions of solids and fluids. The thermal effects of collisions may produce phase change: the example of rain falling on a deeply frozen soil is investigated. Collisions may be so violent that they fracture the bodies: fracturation may also be predicted by the theory. From the theoretical point of view, let us mention that this theory proves that the paradoxes, i.e., illogic results, which are said to result from the equations of mechanics, as the Painlevé-Jellet and Klein paradoxes, may be overcome in a clear and logic manner. Moreover these results are supported by experiments.
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Napoleon Bonaparte's expedition to Egypt in 1798 carried out the first multidisciplinary exploration mission and formed the Institute of Egypt, the first scientific organization in Egypt. A few decades later, the German geographer...
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Napoleon Bonaparte's expedition to Egypt in 1798 carried out the first multidisciplinary exploration mission and formed the Institute of Egypt, the first scientific organization in Egypt. A few decades later, the German geographer and ethnographer Gerhard Rohlfs (1831-1896) led another multidisciplinary expedition in the Western Desert of Egypt. Georg Schweinfurth (1836-1925) independently explored various parts of Egypt over a period of more than fifty years and made major contributions in geology, paleontology, and archeology. The establishment of the Geological Survey of Egypt by the British in 1896 was a turning point in the history of geology in Egypt. The pioneering work of the early staff of the Survey established the solid foundation of the geology of Egypt. Progress in our geological ideas in recent years is credited to the advance in technology, the introduction of new exploration methods, and active international cooperation. A few problems have to be overcome before a real progress in our geological ideas takes place in the future.
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In a recent paper we have studied the peculiar features of the Berry and Aharonov-Anandan geometric phases for isolated spins S≥ 1. We have assumed that they are submitted to a dipole and quadrupole coupling to external E and B f...
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In a recent paper we have studied the peculiar features of the Berry and Aharonov-Anandan geometric phases for isolated spins S≥ 1. We have assumed that they are submitted to a dipole and quadrupole coupling to external E and B fields with the mild restriction E · B = 0. This implies discrete symmetries leading to remarkable simplifications of the geometry and algebra involved. The aim of the present work is to describe realistic proposals, within the realm of atomic physics, for the verification of some of our most significant theoretical predictions. There are several challenges to be overcome. For alkali-metal atoms, most commonly used in atomic interferometers,the only practical way to generate quadrupole coupling, with a strength comparable to the dipole one, is the ac Stark effect induced by a nearly resonant light beam. One then has to face the instability of the" dressed" atom hyperfine (hf) level, a candidate for our isolated spin. One deleterious effect is the apparition of an imaginary part in the quadrupole to dipole coupling strength ratio, A. Fortunately we have found a simple way to get rid of S(λ) by an appropriate detuning. We are left with an unstable isolated spin. This implies an upper bound to the quantum cycle duration T_c. In the case of the Berry's phase, T_c has a lower bound due to the necessity of keeping the nonadiabatic corrections below a predefined level. We have found a compromise in the case of the F = 2,m = 0 ~(87)Rb ground-state hf level. This is our candidate for the measurement of the somewhat "exotic" Berry's phase acquired by the S = 2,m = 0 state at the end of a quantum cycle involving a rotation of π of the E field—in practice, the linear polarization of the dressing beam —about the B field direction. We have found a way to implement, in a Ramsey-type interferometric measurement, the procedures aimed at controlling the nonadiabatic corrections, as described in detail in our previous theoretical paper. A numerical simulation of our experimental proposal shows that a 0.1% accurate determination of Berry's phase, free of nonadiabatic corrections, can be achieved. Measurements could also be considered for cold ~(52)Cr chromium atoms with S =3,where values of 1 can be obtained with an instability smaller than in the 87Rb case, due to a more favorable spectroscopic structure. The F = 1,m = 1 hf level of the ~(87)Rb ground state offers the opportunity to extend the measurement of Aharonov-Anandan's phases beyond the case S = We construct, using "light shift,"the Hamiltonian H_(||) (t) generating a closed circuit in the density-matrix space which satisfies at any time the "parallel transport" condition, thus making the quantum cycle free from the adiabaticity condition. We also consider the case of half-integer spins (e.g., ~(201)Hg ~(135)Ba, and ~(137)Ba), with their own specific features. We show how the difference of Berry's phases for states S =3/2 and S = 1/2, with m = 1/2, can be exploited to achieve a holonomic maximum entanglement of three qubits.
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Representative subsets selected from within larger data sets are useful in many chemoinformatics applications including the design of information-rich compound libraries, the selection of compounds for biological evaluation, and t...
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Representative subsets selected from within larger data sets are useful in many chemoinformatics applications including the design of information-rich compound libraries, the selection of compounds for biological evaluation, and the development of reliable quantitative structure?activity relationship (QSAR) models. Such subsets can overcome many of the problems typical of diverse subsets, most notably the tendency of the latter to focus on outliers. Yet only a few algorithms for the selection of representative subsets have been reported in the literature. Here we report on the development of two algorithms for the selection of representative subsets from within parent data sets based on the optimization of a newly devised representativeness function either alone or simultaneously with the MaxMin function. The performances of the new algorithms were evaluated using several measures representing their ability to produce (1) subsets which are, on average, close to data set compounds; (2) subsets which, on average, span the same space as spanned by the entire data set; (3) subsets mirroring the distribution of biological indications in a parent data set; and (4) test sets which are well predicted by qualitative QSAR models built on data set compounds. We demonstrate that for three data sets (containing biological indication data, logBBB permeation data, and Plasmodium falciparum inhibition data), subsets obtained using the new algorithms are more representative than subsets obtained by hierarchical clustering, k-means clustering, or the MaxMin optimization at least in three of these measures.
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Reversible addition-fragmentation transfer (RAFT) polymerization of a η~5-cyclopentadienylcobalt-η4-cyclobutadiene (CpCoCb) containing monomer under a wide variety of experimental conditions (e.g., different solvents, temperatur...
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Reversible addition-fragmentation transfer (RAFT) polymerization of a η~5-cyclopentadienylcobalt-η4-cyclobutadiene (CpCoCb) containing monomer under a wide variety of experimental conditions (e.g., different solvents, temperatures, RAFT agents, concentrations, and [RAFT agent]/[initiator]) was examined. In all cases the results revealed that although the monomer was being consumed over the course of the reaction, there was no significant increase in the molecular weight of the resulting polymer. It was determined that as the polymer chain grows (DP ≈ 10), a tight coil morphology was adopted, which hinders the approach of an additional, sterically demanding CpCoCb-containing monomer. This resulted in premature termination/chain transfer reactions rather than an increase in the polymer chain length. To address this problem, methyl acrylate (MA) with its lower steric demand was copolymerized with the bulky CpCoCb-containing monomer to act as a spacer. This provided the necessary steric relief and an opportunity for the metallopolymer to grow. This copolymerization resulted in dramatic improvements in the polydispersity and molecular weight of the end material. In subsequent experiments, the random copolymer was used as a macro-RAFT agent to prepare diblock copolymers, with good control over the molecular weight, allowing for an examination of the self-assembly behavior of the block copolymer in the solid state.
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We propose the suppression of dispersive spreading of wave packets governed by the free-space Schr?dinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically dispersionless ...
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We propose the suppression of dispersive spreading of wave packets governed by the free-space Schr?dinger equation with a periodically pulsed nonlinear term. Using asymptotic analysis, we construct stroboscopically dispersionless quantum states that are physically reminiscent of, but mathematically different from, the well-known one-soliton solutions of the nonlinear Schr?dinger equation with a constant (time-independent) nonlinearity. Our analytics are strongly supported by full numerical simulations. The predicted dispersionless wave packets can move with arbitrary velocity and can be realized in experiments involving ultracold atomic gases with temporally controlled interactions.
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Measuring the gravitational behaviour of antimatter is a crucial test of the Weak Equivalence Principle. However, the gravitational force is so weak that the experiment requires a cooling of antimatter never achieved so far. The G...
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Measuring the gravitational behaviour of antimatter is a crucial test of the Weak Equivalence Principle. However, the gravitational force is so weak that the experiment requires a cooling of antimatter never achieved so far. The GBAR experiment aims to overcome this challenge using the anti-ion H~+; a high-intensity positron source has been developed for this purpose.
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Recently we developed a technique for producing cold molecules from a supersonic molecular beam via single collisions with a supersonic atomic beam [M. S. Elioff, J. J. Valentini, and D. W. Chandler, Science 302, 1940 (2003)]. Thi...
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Recently we developed a technique for producing cold molecules from a supersonic molecular beam via single collisions with a supersonic atomic beam [M. S. Elioff, J. J. Valentini, and D. W. Chandler, Science 302, 1940 (2003)]. This cooling technique necessarily produces the cold molecules at the relatively high density crossing of the atomic and molecular beams. In previous reports, secondary glancing collisions with the remnant atomic and molecular beams lead to rapid depletion of the cold molecules limiting the observation time to less than 10 μs with an estimated temperature of 440 mK. Here we present experimental conditions for the kinematic cooling technique which overcome the limitations of the previous experiments. We demonstrate the success of this experiment for the production of cold nitric oxide (NO) in the ground vibrational, j=7.5 rotational, state in order to compare with our previously reported data. With the present setup, we are able to extract the cold molecules from the pulsed molecular and atomic beams and we observe these cold NO(X)_j=7.5 persisting for over 150 μs. This long observation time demonstrates our ability to temporally and spatially separate the cold molecules from the parent atomic and molecular beams, simultaneously allowing for a better measurement of the final average velocity for the kinematically cooled molecules. From the data we find a final average velocity of the NO(X)_j=7.5 of approximately 4.5 m/s, consistent with simulations. The final observed average velocity is equated to a temperature of approximately 35 mK, over an order of magnitude colder than our previous measurements.
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Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equ...
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Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987)]. Our method proceeds directly from the time-dependent Schr?dinger equation and therefore allows various generalizations of the formalism. Second, we obtain an analytic expression for the semiclassical coherent state propagator. We show that the prefactor can be expressed in a form that requires solving significantly fewer equations of motion than in alternative expressions. Third, the semiclassical coherent state propagator is used to formulate a final value representation of the time-dependent wavefunction that avoids the root search, eliminates problems with caustics and automatically includes interference. We present numerical results for the 1D Morse oscillator showing that the method may become an attractive alternative to existing semiclassical approaches.
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