Loop Boundary Research Articles

Fast Loop Boundary Coverage Testing in Symbolic Execution

Symbolic execution is a promising approach for software analyzing and testing, but it still suffers from scalability issues, in which a significant challenge is how to handle loop caused path explosion. This paper proposes a new approach to mitigate the scalability problem brought by loops in symbolic execution. By reusing the previously calculated results captured from satisfiability verification process, we implement a fast loop boundary coverage test strategy which can eliminate a large number of redundant paths and unnecessary solver invocations. Experimental results on Symbolic (Java) PathFinder show that our strategy can greatly improve the efficiency of testing for programs having loops.

Pacman

As caches become larger and shared by an increasing number of cores, cache management is becoming more important. This paper explores collaborative caching, which uses software hints to influence hardware caching. Recent studies have shown that such collaboration between software and hardware can theoretically achieve optimal cache replacement on LRU-like cache. This paper presents Pacman, a practical solution for collaborative caching in loop-based code. Pacman uses profiling to analyze patterns in an optimal caching policy in order to determine which data to cache and at what time. It then splits each loop into different parts at compile time. At run time, the loop boundary is adjusted to selectively store data that would be stored in an optimal policy. In this way, Pacman emulates the optimal policy wherever it can. Pacman requires a single bit at the load and store instructions. Some of the current hardware has partial support. This paper presents results using both simulated and real systems, and compares simulated results to related caching policies.

Spectral properties and low‐dimensional description of loop and recycle reactors

The spectral properties of the discrete and continuous convection and convection‐diffusion operators with loop or recycle boundary condition are analyzed. It is shown that the spectral properties of these nonsymmetric operators are closely related to the theory of circulant (Toeplitz) matrices and the complex Fourier series, respectively. Although there may be many complex eigenvalues, the smallest eigenvalue is real and approaches zero as the loop circulation or recycle ratio increases. This property is used to simplify nonlinear diffusion‐convection‐reaction models of loop and recycle reactors to obtain two‐mode low‐dimensional averaged models that are accurate in the limit of large recycle ratio. Explicit expressions for the two mixing coefficients that relate the two concentration modes and their dependence on various inlet conditions are also derived. Finally, the application of the low‐dimensional models to determine the impact of macromixing on the conversion, yield, and selectivity for the case of nonlinear kinetics is illustrated. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3365–3377, 2013

Steady-State Behavior of Natural Circulation Loops Operating With Supercritical Fluids for Open and Closed Loop Boundary Conditions

Supercritical water (SCW) exhibits excellent heat transfer characteristics and a high volumetric expansion coefficient (hence high mass flow rates in natural circulation systems) near the critical temperature. SCW is being considered as a coolant in some advanced nuclear reactor designs on account of its potential to offer high thermal efficiency, compact size, and elimination of steam generator, separator, and dryer, making it economically competitive. The elimination of phase change results in elimination of the critical heat flux phenomenon. Cooling a reactor at full power with natural instead of forced circulation is generally considered an enhancement of passive safety. In view of this, it is essential to study natural circulation behavior at supercritical conditions. Carbon dioxide can be considered to be a good simulant of water for natural circulation at supercritical conditions, since the density and viscosity variation of carbon dioxide follows a curve parallel to that of water at supercritical conditions. Hence, experiments were conducted in a closed supercritical pressure natural circulation loop (SPNCL) with supercritical carbon dioxide as working fluid. A nonlinear stability analysis code (NOLSTA) has been developed to carry out steady-state and stability analysis of open and closed loop natural circulation at supercritical conditions. The code has been validated for steady-state predictions with experimental data available in open literature and experiments conducted in SPNCL.

Standing Kink Waves with Longitudinal Flow in Fine Threaded Coronal Loops: A New Method for the Coronal Seismology through Beat and Damped Waves

Stimulated by the first weakly attenuated standing kink oscillations of coronal fine threads filled with cool flowing plasma, seen in a recent Ca II H-line observed by Solar Optical Telescope (SOT) aboard Hinode, in this study we present the effects of longitudinal flow on the standing wave. We have found that flow generates two important consequences: first, it produces a frequency shift, which leads to the phenomenon of wave beating; second, it splits the damping time of the forward and backward waves of the attenuated standing wave (considered here only the resonance absorption) into two different values. A comparative analysis of the beat waves, within the “quarter-beat period approximation” together with attenuated waves, seems to be very appealing for coronal seisomology. We refer a new parameter, modulating time ($\tau_{\rm m}$), which is defined as the time when the amplitude of the beat wave becomes zero for a wave train that lies within a quarter period of the beat envelope, the so-called “quarter beat period approximation”. We can compare this $\tau_{\rm m}$ with the attenuating time ($\tau_{\rm D}$) to discriminate the behaviour of the signal, as follows: if $\tau_{\rm m}~\gt~\tau_{\rm D}$, the envelope of the signal is dominated by attenuation due to resonance absorption, while if $\tau_{\rm m}~\lt~\tau_{\rm D}$, the envelope of the signal is dominated by modulation due to beating. Since observation corresponds to first inequality, the amplitude of the signal seems to be dominated by attenuation due to resonance absorption. Hence, the inequality $\tau_{\rm m}~\geq~\tau_{\rm D}$ imposes an upper bounds for the density contrast and magnetic field for a given value of the observed flow. Besides these, we also find that the flow-generated splitting of the damping time also leads to an $\sim\ $8%–10% uncertainty in our estimation of the radial inhomogeneity across the loop boundary, as compared to the static case, i.e., when the flow is zero.

High-Temperature Structural Analysis of a Small-Scale PHE Prototype under the Test Condition of a Small-Scale Gas Loop

A process heat exchanger (PHE) is a key component for transferring the high-temperature heat generated from a very high-temperature reactor (VHTR) to a chemical reaction for the massive production of hydrogen. The Korea Atomic Energy Research Institute has designed and assembled a small-scale nitrogen gas loop for a performance test on VHTR components and has manufactured a small-scale PHE prototype made of Hastelloy-X alloy. A performance test on the PHE prototype is underway in the gas loop, where different kinds of pipelines connecting to the PHE prototype are tested for reducing the thermal stress under the expansion of the PHE prototype. In this study, to evaluate the high-temperature structural integrity of the PHE prototype under the test condition of the gas loop, a realistic and effective boundary condition imposing the stiffness of the pipelines connected to the PHE prototype was suggested. An equivalent spring stiffness to reduce the thermal stress under the expansion of the PHE prototype was computed from the bending deformation and expansion of the pipelines connected to the PHE. A structural analysis on the PHE prototype was also carried out by imposing the suggested boundary condition. As a result of the analysis, the structural integrity of the PHE prototype seems to be maintained under the test condition of the gas loop.

Analysis of dynamic performance of metal rubber damping ring applied in high-speed rotor system

Based on the nonlinearity of metal rubber components and its different elastic damping mechanical properties with different structures, the mechanical model of hysteresis loop boundary deformation process of metal rubber components with different relative densities was established by the experiment method combining theory. Dynamic characteristics of metal rubber damping ring were analyzed under harmonic excitation load and experimental study was conducted. The elastic damping performance of the damper with preliminary deformation was researched and the experimental result showed good agreement with the theoretical analysis one, which provides a theoretical basis for practical application of this kind of damper.

Transverse oscillations of non-planar coronal loops

We suggested a simple model of a non-planar coronal loop (i.e. a loop with torsion). In this model the loop axis is a part of a helical line. Using curvilinear coordinates where the loop axis is a coordinate line and the loop boundary is a coordinate surface we derived the governing equation for the loop kink oscillations. When doing so we have used asymptotic method with the ratio of the loop cross-section radius to the loop curvature radius as a small parameter. The governing equation is exactly the same as one obtained for kink oscillations of a thin straight magnetic tube with the density varying along the tube. This implies that neither the loop curvature nor the loop torsion can directly affect the eigenfrequencies of the loop kink oscillations. They can affect these eigenfrequencies only indirectly through modifying the dependence of the density on the distance along the loop. The main effect of the loop torsion is on the polarization of the loop oscillations. We found that, when we are moving along the loop, the polarization direction is rotating together with the principal normal to the loop axis due to the loop torsion. The application of the obtained results to the interpretation of observations of the loop kink oscillations with a node is discussed.

Fluorinated FeF3 catalyst interactions in three different oil formulations using design of experiment optimization and chemistry characterization of tribofilms

ABSTRACTThe influence of fluorinated FeF3 catalyst on the formation and properties of tribofilms was examined using design of experiment (DOE) under extreme boundary lubrication (385 N or maximum Hertzian contact pressure of 2.72 GPa). A closed loop boundary condition test was developed to examine the behaviour of lubricants under boundary conditions. The reduction of phosphorus in engine oil was examined using two different plain oils and one fully formulated oil. Results indicate the formation of a thicker tribofilm in plain fluorinated oil when compared with fluorinated fully formulated oils.Several chemistry combinations were prepared and tested. Wear and frictional properties were evaluated using DOE, and the interactions of fluorinated FeF3 catalyst with minimum phosphorus were studied and compared with respect to fully formulated and plain zinc dialkyl dithiophosphate oils. Tribofilms with thickness ranging from 150 to 350 nm were developed during wear tests and were analysed for fluorinated plain and fully formulated oils that target reducing phosphorus. Three specific tests with optimised 0.6% FeF3 catalyst concentrations were used with 0.05% phosphorus in plain and fully formulated oil to verify the model optimised conditions with respect to wear and time to full break down. Scanning electron microscopy, hardness of the tribofilms and Auger spectroscopy confirm the presence of fluorine and phosphorus. These tests confirm the optimised prediction of the DOE model. Copyright © 2011 John Wiley & Sons, Ltd.

KELVIN–HELMHOLTZ INSTABILITY IN CORONAL MAGNETIC FLUX TUBES DUE TO AZIMUTHAL SHEAR FLOWS

Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the beta = 0 approximation, and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in time-scales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability.

Analysis of loop boundaries using different local structure assignment methods

Loops connect regular secondary structures. In many instances, they are known to play important biological roles. Analysis and prediction of loop conformations depend directly on the definition of repetitive structures. Nonetheless, the secondary structure assignment methods (SSAMs) often lead to divergent assignments. In this study, we analyzed, both structure and sequence point of views, how the divergence between different SSAMs affect boundary definitions of loops connecting regular secondary structures. The analysis of SSAMs underlines that no clear consensus between the different SSAMs can be easily found. Because these latter greatly influence the loop boundary definitions, important variations are indeed observed, that is, capping positions are shifted between different SSAMs. On the other hand, our results show that the sequence information in these capping regions are more stable than expected, and, classical and equivalent sequence patterns were found for most of the SSAMs. This is, to our knowledge, the most exhaustive survey in this field as (i) various databank have been used leading to similar results without implication of protein redundancy and (ii) the first time various SSAMs have been used. This work hence gives new insights into the difficult question of assignment of repetitive structures and addresses the issue of loop boundaries definition. Although SSAMs give very different local structure assignments capping sequence patterns remain efficiently stable.

Evolution of the current wedge and the generator current circuit by fast reconnection

Temporal dynamics of the generator current circuit and the current wedge is studied on the basis of the spontaneous fast reconnection model. Once the fast reconnection jet causes magnetic field dipolarization, a magnetohydrodynamic (MHD) generator arises ahead of the magnetic loop top. The generator effect is so powerful that a current circuit is strongly driven in the generator region and evolves to approach the loop footpoint through field-aligned currents along the loop boundary; simultaneously, the sheet current directed to the generator region turns its direction toward the loop footpoint, giving rise to current wedge evolution outside the generator current circuit. Both these current circuits are eventually connected to a layer around the separatrix in the loop footpoint, where the current is concentrated and intensified, leading to drastic energy dissipations. It is concluded that the MHD generator ahead of the magnetic loop top, provided and sustained by the fast reconnection jet, plays a crucial role in the two-ribbon heating observed in geomagentic substorms and solar flares.

Impulsive chromospheric heating of two-ribbon flares by the fast reconnection mechanism

Chromospheric heating of two-ribbon flares is quantitatively studied for different values of R0, the ratio of the chromospheric plasma density to the coronal one, on the basis of the spontaneous fast reconnection model. In general, occurrence of impulsive chromospheric joule heating is delayed for the larger R0 because of more Alfvén traveling time in the chromosphere. Once the chromospheric heating occurs, the temperature becomes more than 30 times its initial value for the case of R0=400 in a pair of layers of deep chromosphere, and the region of high temperature shifts upward and becomes broader with time, since the chromospheric thin layer of joule heating shifts upward according to a pileup of reconnected field lines in the flare loop; then, chromospheric evaporation grows and extends outward, and its velocity becomes comparable with the coronal downflow velocity inside the loop boundary. The impulsive chromospheric heating is caused by drastic evolution of the flare current wedge, through which some part of the coronal sheet current suddenly turns its direction to be concentrated into the chromospheric thin layer; simultaneously, a magnetohydrodynamic (MHD) generator arises ahead of the flare loop top to provide a new current circuit inside the large-scale flare current wedge. Hence, it is concluded that the powerful MHD generator, sustained by the fast reconnection jet, drives the flare current wedge to evolve, leading to the impulsive chromospheric heating.

Motion planning and open loop control design for linear distributed parameter systems with lumped controls

Motion planning and open loop boundary control schemes for linear spatially one dimensional distributed parameter systems with lumped control are discussed. Using Mikusiński's operational calculus the models are formulated as ordinary (operational) boundary value problems. Their solutions are parameterized by introducing a so-called basic variable as an appropriate free parameter. Particular classes of models considered lead to series representations involving derivatives of the basic variable of arbitrary order or to convolution operators which can be interpreted as distributed delays and advances. Examples of bending motions on a ring-shaped plate and a heat exchanger illustrate the results.

MODAL ANALYSIS AND DISPERSION CURVES OF A BRAGG FIBER HAVING ASYMMETRIC LOOP BOUNDARY

An analysis of the modal propagation characteristics of a Bragg fiber having asymmetric loop boundary is made, using a simple matrix method. The boundary condition is replaced by matrix equation andthe modal eigen value equation is obtainedunder weak guidance condition. The computed results are shown in the form of d ispersion curves andcutoff frequencies andare comparedwith the dispersion curves of a standard Bragg fiber having circular core cross section. It is seen that the proposedBragg fiber with a small number of claddings (two of four) shows comparable or even better performance than the standard Bragg fiber with respect to a few mode-guidance properties.

Damping of Kink Oscillations in Curved Coronal Loops

We study the kink modes of oscillation of a curved coronal loop using a toroidal model with a power-law density profile. We find that there are two kink modes and that their velocity polarization is either mainly horizontal or mainly vertical with respect to the photosphere. It is found that the damping by resonant absorption in an inhomogeneous layer between the loop and the coronal environment is slightly more efficient than for the straight magnetic cylinder and that the period and damping time of the two kink modes are very similar. In an equilibrium with nonuniform Alfven frequency, the kink modes display two additional features, namely, the coupling to an Alfven mode of the external medium (which gives rise to resonant absorption in the corona) and wave leakage by tunneling at some distance from the loop. Hence, in general the modes are resonantly damped and leaky at the same time, although our results point out that resonant absorption at the loop boundary is the dominant damping mechanism.

A New Approach to Parallelization of Serial Nested Loops Using Genetic Algorithms

Loop parallelization is an important issue in the acceleration of the execution of scientific programs. To exploit parallelism in loops a system of equations representing the dependencies between the loop iterations and a system of non-equations indicating the loop boundary conditions has to be solved. This is a NP-Complete problem. Our major contribution in this paper has been to apply genetic algorithm to solve system of equation and non-equation resulted from loop dependency analysis techniques to find two dependent loop iterations. We use distance vector to find the rest of dependencies.

On Novice Loop Boundaries and Range Conceptions

The paper presents a study of novice difficulties with range conceptions in loop design. CS2 students were asked to solve four related enumeration tasks, which required various loop boundary specifications. The student solutions varied considerably in conciseness and efficiency. The solution diversity reveals significant differences in range partitioning insights. The solutions are categorized, analyzed, and discussed. The categorization and analysis illuminate a novel perspective of novices' lack of range conceptions in loop design. A set of guidelines is offered for addressing this deficiency, by underlining the mathematical and design links between range ends, range partitioning, and loop boundary specifications.

Peculiar behavior of the initial magnetization in CoNi thin films

The initial magnetization curve of ac demagnetized CoNi thin films were outside the hyteresis loop boundary before saturation. Using −dc demagnetization, the initial magnetization curve was brought into the hysteresis loop boundary. Henkel plot shows negative deviation in ac demagnetized CoNi thin film, and both positive and negative deviation, in −dc demagnetized CoNi film. Bitter domain imaging technique showed that the initial magnetization effects are due to the corresponding domain configurations obtained in ac and in −dc demagnetization.

Area distribution of the planar random loop boundary

We numerically investigate the area statistics of the outer boundary of planar random loops, on the square and triangular lattices. Our Monte Carlo simulations suggest that the underlying limit distribution is the Airy distribution, which was recently found to appear also as area distribution in the model of self-avoiding loops.