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The paper deals with complex nonlinear time-dependent material models used in a structure exposed to fast dynamic loading. The finite element solution with the use of the explicit method for the direct integration of equations of motion is provided. Two material models suitable for description of nonlinear response of structure to dynamic loading were developed. These models are based on combination of visco-elastic behavior with the visco-plastic or visco-damage behavior. Behavior of these two models is compared. The behavior of the models under the impact loading is different and the paper shows the results.

This work proposes a chemical mechanism tabulation method using artificial neural networks (ANNs) for turbulent combustion simulations. The method is employed here in the context of the Large-Eddy Simulation (LES)–Probability Density Function (PDF) approach and the method of stochastic fields for numerical solution, but can also be employed in other methods featuring real-time integration of chemical kinetics. The focus of the paper is on exploring an ANN architecture aiming at improved generalization, which uses a single multilayer perceptron (MLP) for each species over the entire training dataset. This method is shown to outperform previous approaches which take advantage of specialization by clustering the composition space using the Self-Organizing Map (SOM). The ANN training data are generated using the canonical combustion problem of igniting/extinguishing one-dimensional laminar flamelets with a detailed methane combustion mechanism, before being augmented with randomly generated data to produce a hybrid random/flamelet dataset with improved composition space coverage. The ANNs generated in this study are applied to the LES of a turbulent non-premixed CH4/air flame, Sydney flame L. The transported PDF approach is used for reaction source term closure, while numerical solution is obtained using the method of stochastic fields. Very good agreement is observed between direct integration (DI) and the ANNs, meaning that the ANNs can successfully replace the integration of chemical kinetics. The time taken for the reaction source computation is reduced 18-fold, which means that LES–PDF simulations with comprehensive mechanisms can be performed on modest computing resources.

In this Letter, we report the direct growth of single crystal III–V thin film mesas on amorphous SiO2 on Si using templated liquid phase growth. Unlike previous works, where crystal sizes demonstrated have been less than ∼10 μm, here, we show that by tuning the crystal growth conditions, crystals with dimensions greater than 100 μm and of high electron mobility can be directly grown on oxides. Specifically, InAs-on-oxide with mobilities reaching 5100 cm2/V s at 100 K, and ∼3200 cm2/V s at room temperature has been demonstrated. The excellent electronic performance is due to the single crystallinity of the grown material and creates new avenues for the monolithic direct integration of high-performance materials on non-epitaxial substrates, including silicon, and amorphous substrates, such as glasses and metals.

The response of nonlinear parametrically excited systems is investigated. It is shown that perturbation methods including the method of multiple scales and the averaging method using the Krylov–Bogoliubov technique can provide precise predictions of the behavior of the system in the neighborhood of the principal parametric resonance. However, increasing the excitation frequency, they imply an infinite growth of the vibration amplitudes, which contradicts numerical and practical findings. To tackle this problem, the method of varying amplitudes (MVA) is used. Employing the MVA, an expression for the upper bound to the displacement response of the system is derived. The parametric excitation frequency, at which this response is attained, is defined explicitly. MVA results considering the first harmonic are identical to the results obtained by the first approximation of the Mitropolskii technique and show good agreement with numerical results obtained from direct integration of the equation of motion. Taking the first and third harmonics into account, MVA shows an excellent capability to capture the frequency at which the upper bound response is attained: the difference between the upper bound to the displacement response obtained from the MVA and the one obtained from numerical integration is less than 0.1%.

The non-conservative nature of the force field generated by a near-field optical trap is analyzed. A plasmonic C-shaped engraving on a gold film is considered as the trap. The force field is calculated using the Maxwell stress tensor method. The Helmholtz-Hodge decomposition is used to extract the conservative and the non-conservative component of the force. Due to the non-negligible non-conservative component, it is found that the conventional approach of extracting the potential by direct integration of the force is not accurate. Despite the non-conservative nature of the force field, it is found that the statistical properties of a trapped nanoparticle can be estimated from the conservative component of the force field alone. Experimental and numerical results are presented to support the claims.

A new method for calculating the conditional scalar dissipation rate 〈N|η〉 is derived from the probability density function (pdf) transport equation for the conserved scalar Z. Two different formulations are obtained. One is the result of direct integration of the pdf transport equation and the second is further developed assuming a two-parameter presumed form for the pdf. A linear model is used for the conditional velocity. The model is compared with a direct numerical simulation (DNS) of inhomogeneous turbulent mixing. The results are in very good agreement with the DNS and perform better than Girimaji’s model which is based on homogeneous flow properties. Further validation with some experimental data would be useful. The new method has also the potential of being easily implemented in a finite-volume computational fluid dynamics code.

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given., 15 pages, 1 figure

The possibility of a solution of the Vlasov–Maxwell equations as a time-dependent problem in a tokamak geometry at ω∼ωci is studied. The major approximations in the analysis are the following: small Larmor radius relative to the wavelength, particle orbits deviate little from a magnetic surface during the time of the dominant contribution to the orbit integral. This direct integration becomes possible due to a rapid growth of the computing power and the development of multiprocessing. A proper description of the plasma dielectric properties in this time-dependent approach is made. Due to a limited computing power and not completely optimized procedure applied in the analysis, the time evolution of Maxwell equations is limited to cases of relatively small perpendicular wave numbers. The results demonstrate that it is computationally feasible to perform a direct integration of the time-dependent Vlasov–Maxwell equations in a tokamak geometry on a substantially long time interval. The directions of the furth...

We present a semiclassical method for simulating the dynamics of nonadiabatic transitions in a discrete-state quantum system coupled to a bath of explicit continuous coordinates. This method employs a coherent-state formulation of the path integrals for the discrete system whose dynamics is described by spin operators. This spin coherent-state formulation allows the discrete system to be mapped onto a continuous coordinate. Stationary approximations of the resulting coherent-state path integrals of the system plus bath lead to quasiclassical equations of motion which can be solved numerically by direct integration. This algorithm reduces the problem to a number of simple classical trajectory calculations and does not require calculating any fluctuation determinants.

An accurate theory of two‐photon dissociation with strong laser pulses, which goes beyond the adiabatic approximation, is developed. Criteria for adiabatic behavior in two photon dissociation (enabling via adiabatic passage the complete population transfer to the continuum), are derived. We obtain the minimal pulse duration needed to ensure adiabaticity as a function of the field intensities and detuning. In addition, we develop a simple, rapidly converging, iterative scheme, built on the adiabatic approximation, for the exact solution of the two‐photon dissociation problem. Each iteration step requires a computational effort that scales as N2 (N being the system dimension) for full matrices, or N log N for sparse matrices. The iterative scheme is tested by comparing it to the Runge–Kutta–Merson direct integration algorithm. It is found to work well even when the adiabatic approximation fails completely.

The beam deflection coefficients to the magnetic field fluctuation using a gold neutral beam probe was examined by numerical simulations. The beam deflection parallel to the magnetic field line was mainly caused by the azimuthal component of the magnetic field fluctuation in a case of the beam passing through the plasma center; on the other hand, the beam passing through the plasma edge was deflected by the radial component of the magnetic field fluctuation because the radial and azimuthal velocity components of the beam depend on the injection angle into the plasma. Then, the coefficients could be described as being the function of the injection angle which indicated the radial position of the ionization point and the measured point. As a result of numerical simulation, the coefficients were estimated to be 0.1 and 1.3 for the radial and the azimuthal components of the magnetic field fluctuation in the case of the beam passing through the plasma center. We also estimated the potential effects on the beam...

We present a resonant mass sensor for specific biomolecular detection in a subnanoliter fluid volume. The sensing principle is based on measuring shifts in resonance frequency of a suspended microfluidic channel upon accumulation of molecules on the inside walls of the device. Confining the fluid to the inside of a hollow cantilever enables direct integration with conventional microfluidic systems, significantly increases sensitivity by eliminating high damping and viscous drag, and allows the resonator to be actuated by electrostatic forces. Fluid density measurements reveal a mass resolution of 10−17 g/μm2 in a 4 mHz–4 Hz bandwidth. To demonstrate biomolecular detection, we present real-time measurements of the specific binding between avidin and biotinylated bovine serum albumin. Based on these measurements, we expect that changes in surface mass loading on the order of 10−19 g/μm2 can be detected in an optimized system.

Three-dimensional magnetic structures of pi-vertical-Bloch line (VBL) and 2pi-VBL are investigated in 80–320-nm-thick Permalloy films using direct integration of the Landau–Lifshitz–Gilbert equation in an 128×128×80 point Cartesian lattice. A pi-VBL reflects the shapes of its adjacent walls, which change with film thickness. The pi-VBL conducts the flux between walls of opposite chirality by letting the magnetization rotate out of the plane of the walls via a vortex structure. The Neel caps switch chirality via a “converging point,” or cross-tie, flux at one surface and a vortex flux, or a swirl, at the other surface. The pi-VBL energy per unit area is 0.44, 0.20, and 0.30 erg/cm2 in 80, 160, and 320 nm films, respectively. The corresponding pi-VBL widths are 88, 60, and 86 nm. A stable winding 2pi-VBL structure was also computed by combining two pi-VBL structures of appropriate chirality. The Neel caps intersect via the pair-(swirl, converging point) like flux at both surfaces. The width of the 2pi-VBL i...

Various versions of the complex coordinate method are applied to the characterization (positions and widths) of the Slonczewski resonances associated with the conical intersections of a E⊗e Jahn–Teller system in the linear approximation and strong coupling regime. The procedure is based on the direct integration of the coupled differential equations either in a diabatic or in an adiabatic formulation, with imposition of appropriate boundary conditions. Complex rotation of the radial coordinate changes the real eigenenergies of this bound system into complex ones with imaginary parts giving rate constants. Various checks on the significance of these energies are made. Pade approximants are used to relate them to the results of Slonczewski obtained under the assumption of zero restoring force.

Two methods for the construction of alternative Lagrangians to the standard Lagrangian L=T−V where V is a central potential are presented: the direct integration of the Hessian matrix and the use of the Noether symmetries of L. The Lagrangians obtained are of the so‐called nonlinear homogenous (NLH) type and the study is centered in those Lagrangians not preserving the spherical symmetry of L. Finally, the associated Hamiltonian formalism is presented.

The generalized Langevin equation (GLE) has been used to model a wide variety of systems in which a subset of the degrees of freedom move on a potential of mean force surface subject to fluctuating forces and dynamic friction. When there is a wide separation in the time scales for motion on the potential surface and for relaxation of the friction kernel, direct integration of the GLE is very costly in CPU time. In this paper we introduce an integrator based on our previous work using numerical analytical propagator algorithm (NAPA) and reference system propagator algorithm (RESPA) that greatly accelerates such simulations. We also discuss sampling methods for the random force. Accuracy of this algorithm is assessed by comparisons with an analytically solvable example. Introducing dynamic friction kernels determined from full molecular dynamics (MD) simulations allows us to compare the accuracy of the GLE simulations with full scale molecular dynamics simulations.

Direct integration of the Landau–Lifshitz–Gilbert equation in a three-dimensional rectangular lattice shows that fabrication asymmetry of tapered ends affects the magnetic switching behavior of the magnetic layers of a pseudospin valve (PSV) memory cell in word disturb condition. When a 10 nm asymmetry is introduced with the longer sides of the tapers on the same side of the PSV memory cell, a “360°” wall in the storage layer is formed when a 40 Oe uniform word disturb field is applied opposite to the magnetization direction in the storage layer. The initial magnetization state is recovered when the field is turned off. When the longer sides of the tapers are on opposite sides of the cell, complete magnetization reversal occurs in the storage layer. The sense layer and the storage layer relax to an antiparallel configuration magnetization that is opposite to the initial configuration in the memory cell when the field is turned off. The information is lost. Successful operation of the memory depends upon a...

A first principles quantum-mechanical method for estimating intrinsic breakdown strength of insulating materials has been implemented based on an average electron model which assumes that the breakdown occurs when the average electron energy gain from the electric field exceeds the average energy loss to phonons. The approach is based on density functional perturbation theory and on the direct integration of electronic scattering probabilities over all possible final states, with no adjustable parameters. The computed intrinsic breakdown field for several prototypical materials compares favorably with available experimental data. This model also provides physical insight into the material properties that affect breakdown.

Stoney’s equation allows one to calculate the internal stress in a thin film deposited on a thick substrate from the curvature of the bilayer beam. The curvature measurement is thus critical in the bending beam method, which is based on this equation. When an optical technique is used in curvature measurement, the refraction at optical boundaries needs to be corrected. An approximate correction to Stoney’s equation accounting for refractive error in the bending beam method in electrochemical applications was reported previously. This paper revisits the derivation. A set of diagrams for optical paths in in situ curvature measurement using the laser beam deflection method are presented. These diagrams allow us to establish the triangular relationships among the incident angles of the light beam and the deflection angle of the cantilever beam. Correction solutions are derived for three possible optical arrangements with the consideration of the travel distance of the light beam in liquid and in the container wall. In its approximated form, the correction derived in this paper differs from the previous formula by a factor of 2. It was discovered that an incorrect relationship for curvature was used in the previous derivation.

Doped and intrinsic Ge1−x−ySixSny alloys are synthesized directly on Si(100) using simple deposition chemistries and their optical and electrical properties are determined. Tuning the Si/Sn ratio at ∼4 yields strain-free films with Ge-like cell dimensions, while variation of the ratio around this value produces compressively strained, tetragonal structures with an in-plane lattice constant “pinned” to a value close to that of pure Ge (5.658 A). First-principles calculations show that mixing entropy thermodynamically stabilizes SiGeSn in contrast to GeSn analogs with the same Sn content. GeSn and SiGeSn are predicted to become metastable for 2% and 12% Sn, respectively, in good agreement with experiment.

The direct integration of light and optical control into microfluidic systems presents a significant hurdle to the development of portable optical trapping-based devices. A simple, inexpensive fiber-based approach is provided that allows for easy implementation of diode-bars for optical particle separations within flowing microfluidic systems. Models have also been developed that demonstrate the advantages of manipulating particles within flow using linear geometries as opposed to individually focused point traps as traditionally employed in optical-trapping micromanipulation.

The Kepler problem is a dynamical system that is well defined not only on the Euclidean plane but also on the sphere and on the Hyperbolic plane. First, the theory of central potentials on spaces of constant curvature is studied. All the mathematical expressions are presented using the curvature $\k$ as a parameter, in such a way that they reduce to the appropriate property for the system on the sphere $S^2$, or on the hyperbolic plane $H^2$, when particularized for $\k>0$, or $\k, 37 pages, 7 figures

Domain wall mobility in Permalloy films has been calculated as a function of thickness at 10, 80, and 160 nm which reflects the structure change of Neel, symmetric Bloch and C-shaped (asymmetric Bloch) domain walls. The mobility has been derived from the dynamics of a single nonperiodic domain wall using direct integration of the Landau–Lifshitz–Gilbert equation in a Cartesian lattice. This investigation allows for a detailed examination of spin precession, wall motion and overall magnetization distortion as the wall is moved in the presence of fields ranging from 0.5 to 5 Oe applied in the easy axis direction. At 10-nm-thick films, the mobility of a Neel wall is 30 m/s Oe. Wall motion takes place without noticeable distortion in the magnetization distribution in the vicinity of the Neel wall. For 80 nm-thick films, the mobility of a symmetric Bloch wall is 5 m/s Oe, or 20% less than the theoretical prediction for the mobility of a 180° domain wall model. At dynamic equilibrium, the symmetric Bloch wall h...

The three possible transitions of a wall involving a change of chirality and position of a vortex were previously identified in Permalloy™ using the Kerr effect. These transitions have now been simulated using direct integration of the Landau–Lifshitz–Gilbert equation in a 1 300 000 point Cartesian lattice. One transition is between two C-shaped, same chirality walls whose vortices are on opposite sides. The transition is done via a 32-nm-long pi-VBL structure at the surfaces and at the center via a shape transition 117 nm long. The pi-vertical Bloch line (pi-VBL), which changes chirality along the wall, conducts the flux between the walls of opposite chirality via a vortex structure by letting the magnetization rotate out of the plane of the walls at the center of this vortex. The Neel caps switch chirality via an antivortex flux at one surface and a vortex flux at the other surface. Another transition is a pi-VBL that takes place between two C-shaped, opposite chirality walls whose vortices are on oppos...

MicroMAG‐2D (version 2.0) system has been developed for investigations of statics and dynamics of two‐dimensional 180° domain walls in the thin ferromagnetic films with arbitrary uniaxial anisotropy. This system is intended for developers of magnetic memory devices, physicists (experimentators and theoreticians), and may be used for illustration at high school (university) educational process. Static structure is a result of solving of nonlinear variational micromagnetic problem with magnetostatic interaction. Domain wall dynamics is computed by direct integration of Landau–Lifshits–Gilbert equation. Computational method used fast algorithm for demagnetization field and unconditionally stable scheme for temporal integration. Domain wall is keeping in the center of computational region by shadowing method.1 MicroMAG‐2D system consists of (a) initial data generation module; (b) computational module; (c) Editor/Viewer module; (d) Animator module. System requirements: IBM PC AT compatible (Intel 80386/387 or ...

The two particle diffusion controlled reaction rate with Smoluchowski boundary conditions is derived by direct integration of the diffusion equation in the long time limit, together with an integral equation for the spatial part of the long time probability function. In a first order approximation this rate constant takes the value of the exact inverse mean first passage time. It is also shown how to obtain from the two particle result the rate constant for N concurrent independent two particle reactions between unbound particles. A new derivation is given of the mean first passage time in the Wilemski–Fixman closure approximation which clarifies the differences between the boundary conditions and sink term methods. Our previous statement that the exact and closure approximation results coincide to the third term of the expansion in the reaction sink radius is confirmed.

We have studied the contrast of a stacking fault in the Laue‐Bragg case, i.e., when the wave fields incident from the defect are reflected from its surface and never propagate into the other part of the crystal. To calculate the contrast of such a defect we have computed the images by a direct integration of Takagi’s equations. We show the influence of different parameters such as the geometry of the fault, the fault vector, and the photoelectric absorption. The results are very similar to those obtained by Authier in the Laue‐Laue case and the contrast may be explained in a similar manner.

The equations for the thermodynamic potentials of the solvent in solutions of ordinary organic molecules are extended to solutions of large molecules by methods using continuous molecular distribution functions. Particular attention is given to the coefficient, A2, of the second term in the expansion of the osmotic pressure in terms of the concentration, since this coefficient has a simple molecular meaning and is sufficient to describe the deviation of the system from ideality at low concentrations. A2 is calculated by direct integration for two rigid shapes, the sphere and the long thin rod. A general expression is then developed for A2 for flexible chain molecules in terms of the interactions of the segments of the chains. In favorable cases it is found possible to relate A2 for a chain molecule to the solution properties of its small molecule homologues by an equation very similar to those developed by Flory, Huggins, and Miller. In general, however, interactions that depend both on the local structur...

The radial distribution functions g for a system of particles interacting with the Lennard‐Jones 6–12 potential have been found by solving the Percus—Yevick (PY) equation, convolution approximation or hypernetted chain equation (CHNC), and the Born—Green—Yvon (BGY) equation, for four particle densities already investigated by Monte Carlo (MC) techniques by Wood and Parker. The thermodynamic quantities p/nkT, E/NkT, and nkTK have also been computed from the g's. A comparison shows that the PY quantities agree best with MC, CHNC quantities agree next best, and BGY agree most poorly, particularly at high densities. A comparison of nkTK computed by differentiating p/nkT and by direct integration involving g gives approximately consistent results for the PY g but not for the CHNC g. The asymptotic form of g for high densities for the PY and CHNC equations is found to agree with that obtained by Kirkwood.

Formulas are derived, by direct integration of the defining definite integrals, for the general geometric mean distance between (i) a point and a line segment; (ii) a point and a rectangular area; (iii) two parallel line segments; (iv) two orthogonal line segments; (v) a line segment and a parallel‐sided rectangular area; (vi) two parallel‐sided rectangular areas. Certain useful identities of the formula for the last‐named case are presented.

The difference which is present between the semi‐ and the nonempirical value of a Slater‐Condon parameter (SCP) is discussed. It is pointed out that the nonempirical value which is to be compared with its semiempirical counterpart, must be determined with the same least‐squares method as that used in the determination of the semiempirical values, by treating the Hartree‐Fock (HF) total energy of each state of a configuration as the term value of the respective state, although it is usually determined for each of the states by a direct integration using the HF AO's appropriate to respective states. The data for the atoms and the ions having the electron configurations of 1s22sm2pn type show that the nonempirical value of an SCP thus determined for a particular configuration is more or less the same as that is obtained as the weighted mean of the values of the parameter determined for various states belonging to the configuration by integrations using HF AO's. The difference between the nonempirical value o...

The magnetic flux threading a general pickup coil system is expressed as a power series expansion in which the source and detector dependencies are separated. Specific expressions are developed for the commonest coil system—a single circular coil. For a given configuration, the maximum error is simply related to the number of terms retained in the expansion. Actual computations show that, for a single circular coil, and for configurations typically encountered in biomagnetic studies, the power series expansion method is about 20 times faster than direct integration of the vector potential over the coil perimeter.

The standard basis operator (SBO) equation of motion is solved exactly for the class of interacting many‐body Hamiltonians which can be constructed from a complete set of mutually orthogonal projection operators. This class includes the Ising model Hamiltonians. Two integration procedures are presented: (1) term by term integration over the poles of the SBO double‐time temperature‐dependent Green’s functions in the spectral representation; (2) direct integration of the time‐dependent equation of motion of an SBO. An ensemble average expression relating correlation functions among systems in different energy states is derived. For the Ising model this expression relates correlation functions of spin clusters of different orders, and it is analogous to a relation derived from the master equation under equilibrium conditions.

A novel technique for determining the energies of bound and resonant states of semiconductor structures is presented. The new method is based upon R‐matrix propagation techniques (known to be numerically stable) and avoids direct integration of the Schrodinger equation. The new method is recursive in nature, numerically stable, and can be applied easily to any one‐dimensional potential. We show that the new technique yields the well‐known analytic results describing the energy spectrum of a single quantum well. Further examples illustrate application of the R‐matrix technique to determine the bound state and resonant energy spectrum of multiple quantum well structures in the presence or absence of an applied bias.

A variation-perturbation technique is outlined as an alternative to the ordinary time-dependent perturbation method. The essential point of the technique is to factor out the effective time dependence of the perturbed wavefunction and to reduce the remaining problem to the solution of time- dependent inhomogeneous differential equations. For simple cases a direct integration is possible, while a variational approach is applicable to more complex equations. (P.C.H.)

A direct integration approach coupled with Newton’s iteration scheme was devised to determine the linear stability of a hydrodynamic system with general boundary conditions. A fundamental set of linearly independent solutions was constructed whose coefficients are to be determined by the boundary conditions. In order to assure the existence of nontrivial solutions for the coefficients, a secular equation must be solved whose solution determines the stability criteria to an arbitrary degree of accuracy. This method was applied to a two‐component liquid system with rigid‐rigid boundaries and an imposed temperature gradient. No approximation was made of the Soret‐effect term and of the primary‐state configuration. A slope discontinuity was found in the critical Rayleigh number as the Soret coefficient increases in the positive region. The frequency of the oscillatory mode was found to be very sensitive to the variation of the negative Soret coefficient near the bifurcation point, and to the variation of the concentration near zero or unity. Comparison with existing experiments is also discussed.

Using an initial smoothed random velocity distribution a comparison is made between results obtained by direct integration of Burgers' equation and those obtained by application of Kraichnan's Lagrangian‐history direct‐interaction approximation to this equation.