Direct versus measurement assisted bipartite entanglement in multi-qubit systems and their dynamical generation in spin systems

We consider multi-qubit systems and relate quantitatively the problems of generating cluster states with high value of concurrence of assistance, and that of generating states with maximal bipartite entanglement. We prove an upper bound for the concurrence of assistance. We consider dynamics of spin-1/2 systems that model qubits, with different couplings and possible presence of magnetic field to investigate the appearance of the discussed entanglement properties. We find that states with maximal bipartite entanglement can be generated by an XY Hamiltonian, and their generation can be controlled by the initial state of one of the spins. The same Hamiltonian is capable of creating states with high concurrence of assistance with suitably chosen initial state. We show that the production of graph states using the Ising Hamiltonian is controllable via a single-qubit rotation of one spin-1/2 subsystem in the initial multi-qubit state. We shown that the property of Ising dynamics to convert a product state basis into a special maximally entangled basis is temporally enhanced by the application of a suitable magnetic field. Similar basis transformations are found to be feasible in the case of isotropic XY couplings with magnetic field.Comment: (14 pages, 7 figures, RevTeX4

Unified Structural Representation of the southern California crust and upper mantle

We present a new, 3D description of crust and upper mantle velocity structure in southern California implemented as a Unified Structural Representation (USR). The USR is comprised of detailed basin velocity descriptions that are based on tens of thousands of direct velocity (Vp, Vs) measurements and incorporates the locations and displacement of major fault zones that influence basin structure. These basin descriptions were used to developed tomographic models of crust and upper mantle velocity and density structure, which were subsequently iterated and improved using 3D waveform adjoint tomography. A geotechnical layer (GTL) based on Vs30 measurements and consistent with the underlying velocity descriptions was also developed as an optional model component. The resulting model provides a detailed description of the structure of the southern California crust and upper mantle that reflects the complex tectonic history of the region. The crust thickens eastward as Moho depth varies from 10 to 40 km reflecting the transition from oceanic to continental crust. Deep sedimentary basins and underlying areas of thin crust reflect Neogene extensional tectonics overprinted by transpressional deformation and rapid sediment deposition since the late Pliocene. To illustrate the impact of this complex structure on strong ground motion forecasting, we simulate rupture of a proposed M 7.9 earthquake source in the Western Transverse Ranges. The results show distinct basin amplification and focusing of energy that reflects crustal structure described by the USR that is not captured by simpler velocity descriptions. We anticipate that the USR will be useful for a broad range of simulation and modeling efforts, including strong ground motion forecasting, dynamic rupture simulations, and fault system modeling. The USR is available through the Southern California Earthquake Center (SCEC) website (http://www.scec.org)

Some effects of the initiator on the cationic polymerization of alkenes

The content of this article is indicated by what could be its full title: “An Explanation of the dependence of the rate of the cationic polymerizations of alkenes and of the DP of their products, on the reaction variables, especially the size of the anionic moiety of the initiator.” We continue here the discussion started in 1965 and show mathematically how the theory of dieidic polymerizations by unpaired and paired cations can explain why some of these polymerizations become faster with falling temperature, why the Arrhenius plot of the DP of the polymers obtained from most such systems shows a discontinuity or kink, and also how the temperature of minimum rate, TM, and that at which the kink occurs, TK, depend on the reaction variables, namely the concentrations of monomer, m, and of initiator, c, and the a, D, and T (interionic distance in the ion-pair, dielectric constant of the reaction mixture and temperature). Our treatment explains why the most effective way of achieving the economically desirable aim, to make the longest polymers at the highest possible temperatures, is by maximizing the product a.D, so as to increase the TK, preferably by the use of polar solvents and initiators with large anions. The choice of such combinations by several investigators, but for other, vaguer, reasons, is given here a theoretical basis. Our argument is illustrated by Literature examples and is presented in the form of a new diagram (the Plesch-Austin plot) which shows the TK as a function of a.D for several systems. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4265–4284, 200

Defining Proper Boundary Conditions in 3-D Structural Restoration: A Case Study Restoring a 3-D Forward Model of Suprasalt Extensional Structures

International audienceTo overcome the non-physical limitations to 2D structural restoration tools, efforts are being made toward developing 3D mechanics-based methods, which respect both mass and linear momentum conservations. 3D methods remove many common assumptions in 2D techniques that are often violated in nature, such as line-length and area conservation or constant boundary condition (BC) displacement. However, 3D restorations have challenges of their own that must be overcome to produce accurate, physical representations of rock deformation. One of the greatest challenges is choosing geologically and physically reasonable BCs. These are often based on accepted geometric assumptions, such as flattening and unfolding a datum horizon while simultaneously removing fault offset. However, these BCs, as based on kinematic hypotheses, may lead to unphysical configurations. In addition, non-physical BCs are often required in order to ensure numerical convergence (e.g. fixing degrees of freedom), adding uncertainty to the result. Understanding the forward deformation process is crucial for defining proper BCs and accurate interpretations of a restoration. In this study, we perform a 3D restoration on the structures formed from a 3D analog model. Restoring a forward model provides a priori knowledge of viable BCs to guide our restorations without adding unknown uncertainty to the result. The analog experiment was a 3D forward model of a gravity-driven extensional system with sand layers above a ductile zone, no pre-existing fault architecture and a 1.5° basinward dip. Sedimentary layers were added as growth strata throughout the forward model, recording the timing and kinematics of fault activity and fold growth. The analog model produced two prominent grabens, several half-grabens, salt welds and secondary fault structures. Using BCs defined from knowledge of the undeformed and deformed states, we perform a sequential 3D restoration of this extensional system. These BCs at each time-step are constrained by video capturing the complete forward deformation sequence. These findings are the first to document how accurate BCs add value to 3D restoration techniques. Moreover, restoring the complex structures in our model provides fundamental insight into the temporal evolution of 3D extensional structures, akin to natural suprasalt basins like GOM, Brazil and Angola. This clears the path for increasing accuracy in strain evaluation and assessment of paleo-basin geometry

Defining Proper Boundary Conditions in 3-D Structural Restoration: A Case Study Restoring a 3-D Forward Model of Suprasalt Extensional Structures

International audienceTo overcome the non-physical limitations to 2D structural restoration tools, efforts are being made toward developing 3D mechanics-based methods, which respect both mass and linear momentum conservations. 3D methods remove many common assumptions in 2D techniques that are often violated in nature, such as line-length and area conservation or constant boundary condition (BC) displacement. However, 3D restorations have challenges of their own that must be overcome to produce accurate, physical representations of rock deformation. One of the greatest challenges is choosing geologically and physically reasonable BCs. These are often based on accepted geometric assumptions, such as flattening and unfolding a datum horizon while simultaneously removing fault offset. However, these BCs, as based on kinematic hypotheses, may lead to unphysical configurations. In addition, non-physical BCs are often required in order to ensure numerical convergence (e.g. fixing degrees of freedom), adding uncertainty to the result. Understanding the forward deformation process is crucial for defining proper BCs and accurate interpretations of a restoration. In this study, we perform a 3D restoration on the structures formed from a 3D analog model. Restoring a forward model provides a priori knowledge of viable BCs to guide our restorations without adding unknown uncertainty to the result. The analog experiment was a 3D forward model of a gravity-driven extensional system with sand layers above a ductile zone, no pre-existing fault architecture and a 1.5° basinward dip. Sedimentary layers were added as growth strata throughout the forward model, recording the timing and kinematics of fault activity and fold growth. The analog model produced two prominent grabens, several half-grabens, salt welds and secondary fault structures. Using BCs defined from knowledge of the undeformed and deformed states, we perform a sequential 3D restoration of this extensional system. These BCs at each time-step are constrained by video capturing the complete forward deformation sequence. These findings are the first to document how accurate BCs add value to 3D restoration techniques. Moreover, restoring the complex structures in our model provides fundamental insight into the temporal evolution of 3D extensional structures, akin to natural suprasalt basins like GOM, Brazil and Angola. This clears the path for increasing accuracy in strain evaluation and assessment of paleo-basin geometry