Problem Of Pattern Selection Research Articles

Critical Pattern Selection Method Based on CNN Embeddings for Full-Chip Optimization

Source mask optimization (SMO), a primary resolution enhancement technology, is one of the most pivotal technologies for enhancing lithography imaging quality. Due to the high computation complexity of SMO, patterns should be selected by a selection algorithm before optimization. However, the limitations of existing selection methods are twofold: they are computationally intensive and they produce biased selection results. The representative method having the former limitation is the diffraction signature method. And IBM’s method utilizing the rigid transfer function tends to cause biased selection results. To address this problem, this study proposes a novel pattern cluster and selection algorithm architecture based on a convolutional neural network (CNN). The proposed method provides a paradigm for solving the critical pattern selection problem by CNN to transfer patterns from the source image domain to unified embeddings in a K-dimensional feature space, exhibiting higher efficiency and maintaining high accuracy.

Cross-diffusion effects on stationary pattern formation in the FitzHugh-Nagumo model

<p style='text-indent:20px;'>We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the existence of a double bifurcation threshold of the inhibitor/activator diffusivity ratio for the onset of patterning instabilities: for large values of inhibitor/activator diffusivity ratio, classical Turing patterns emerge where the two species are in-phase, while, for small values of the diffusion ratio, the analysis predicts the formation of out-of-phase spatial structures (named <i>cross-Turing patterns</i>). In addition, for increasingly large values of the inhibitor cross-diffusion, the upper and lower bifurcation thresholds merge, so that the instability develops independently on the value of the diffusion ratio, whose magnitude selects Turing or cross-Turing patterns. Finally, the pattern selection problem is addressed through a weakly nonlinear analysis.</p>

Capturing software architecture knowledge for pattern-driven design

Context:Software architecture is a knowledge-intensive field. One mechanism for storing architecture knowledge is the recognition and description of architectural patterns. Selecting architectural patterns is a challenging task for software architects, as knowledge about these patterns is scattered among a wide range of literature. Method:We report on a systematic literature review, intending to build a decision model for the architectural pattern selection problem. Moreover, twelve experienced practitioners at software-producing organizations evaluated the usability and usefulness of the extracted knowledge. Results:An overview is provided of 29 patterns and their effects on 40 quality attributes. Furthermore, we report in which systems the 29 patterns are applied and in which combinations. The practitioners confirmed that architectural knowledge supports software architects with their decision-making process to select a set of patterns for a new problem. We investigate the potential trends among architects to select patterns. Conclusion:With the knowledge available, architects can more rapidly select and eliminate combinations of patterns to design solutions. Having this knowledge readily available supports software architects in making more efficient and effective design decisions that meet their quality concerns.

A random utility based estimation framework for the household activity pattern problem

This paper develops a random utility based estimation framework for the Household Activity Pattern Problem (HAPP). Based on the realization that outputs of complex activity-travel decisions form a continuous pattern in space-time dimension, the estimation framework is treated as a pattern selection problem. In particular, we define a variant of HAPP that has capabilities of forecasting activity selection and durations in addition to activity sequencing. The framework is comprised of three steps, (i) choice set generation, (ii) choice set individualization and (iii) model estimation. The estimation results show that utilities for work, shopping and disutilities for travel time, time outside home, and average tour delay are found to be significant in activity-travel decision making.

How pattern is selected in drift wave turbulence: Role of parallel flow shear

The role of parallel shear flow in the pattern selection problem in drift wave turbulence is discussed. Patterns of interest here are E × B convective cells, which include poloidally symmetric zonal flows and radially elongated streamers. The competition between zonal flow formation and streamer formation is analyzed in the context of modulational instability analysis, with the parallel flow shear as a parameter. For drift wave turbulence with k⊥ρs ≲ O(1) and without parallel flow coupling, zonal flows are preferred structures. While increasing the magnitude of parallel flow shear, streamer growth overcomes zonal flow growth. This is because the self-focusing effect of the modulational instability becomes more effective for streamers through density and parallel velocity modulation. As a consequence, the bursty release of free energy may result as the parallel flow shear increases.

A Random Utility Based Estimation Framework for the Household Activity Pattern Problem

Abstract: This paper develops a random utility based estimation framework for the Household Activity Pattern Problem (HAPP). Based on the realization that outputs of complex activity-travel decisions form a continuous pattern in space-time dimension, the estimation framework is treated as a pattern selection problem. In particular, we define a variant of HAPP that has capabilities of forecasting activity selection and durations in addition to activity sequencing. The framework is comprised of three steps, (i) choice set generation, (ii) choice set individualization and (iii) model estimation. The estimation results show that utilities for work, shopping and disuilities for travel time, time outside home, and average tour delay are found to be significant in activity-travel decision making.

Pattern selection in a horizontally vibrated container

We present results of an experimental and numerical investigation of the patterns realized by surface waves within an open rectangular container subjected to horizontal vibrations at frequencies of 40–100 Hz. The first instability exhibited by the primary harmonic wave field is subharmonic, and may be identified with the cross-wave instability often seen in wave tank experiments. We show that, contrary to common theoretical and experimental assumptions, and despite their name, these subharmonic waves are not oriented crosswise, but at an intermediate angle with respect to the axis of vibration. Hence, the pattern selection problem for horizontally forced Faraday waves is more complex than has previously been assumed. We establish the robustness of this obliquely oriented surface wave pattern by varying the forcing frequency and amplitude, the fluid viscosity, the fluid depth, and the boundary conditions. Previous work on cross-waves is reviewed and discussed in relation to the current results. Finally, numerical simulations using a reduced model with an appropriate forcing term are used to support the generality of the experimental observations.

The effect of noise on patterns formed by growing sandpiles

We consider patterns generated by adding large numbers of sand grains at a single site inan Abelian sandpile model with a periodic initial configuration, and relaxing. The patternsshow proportionate growth. We study the robustness of these patterns against differenttypes of noise, namely, randomness in the point of addition, disorder in the initial periodicconfiguration, and disorder in the connectivity of the underlying lattice. We find that thepatterns show a varying degree of robustness to addition of a small amount of noisein each case. However, introducing stochasticity in the toppling rules seems todestroy the asymptotic patterns completely, even for a weak noise. We also discussa variational formulation of the pattern selection problem for growing Abeliansandpiles.

Pattern selection in parametrically driven arrays of nonlinear resonators

We study the problem of pattern selection in an array of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems, using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [Phys. Rev. E 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude is varied either quasistatically, abruptly, or as a linear ramp in time. We find interesting hysteretic effects, which are confirmed by numerical integration of the original equations of motion of the interacting nonlinear resonators.

Cropping pattern planning under water supply from multiple sources

Conventionally, irrigation development planning has been based on cropping pattern selection aiming at maximizing the revenue from irrigation activities. In the real world however, several complexities make the cropping pattern selection a more complicated mathematical problem. Of great interest is the case of water supply from multiple sources (e.g. surface and groundwater) in which a multi-criteria approach is most appropriate. Goal programming has been used in the past to solve cropping pattern selection problems, with criteria of a similar nature, the net benefit being included as a constraint. This paper presents a methodology, based on the fuzzy set theory, for enhancing the goal programming approach to solve similar problems under various sets of criteria of a different nature. In the proposed methodology the net benefit maximization is considered together with all other criteria. The methodology is illustrated using data from the Thessaly Plain in Greece.

Transition to turbulence in open flows: what linear and fully nonlinear local and global theories tell us

Mixing layers, jets, wakes, boundary layers over wings or rotating disks, Poiseuille and Couette flows are examples of open shear flows encountered in many industrial or geophysical situations. These flows develop spatially under the combined action of advection and instabilities and eventually undergo a transition to turbulence. In the eighties, the linear concepts of absolute and convective instability succeeded in predicting some aspects of open shear flow dynamics, but a description of their spatio-temporal development including nonlinear effects and secondary instabilities was lacking and even the very fact that a linear criterion describes so well strongly nonlinear flows remains mysterious. The present work reports on very recent progress elucidating open shear flow dynamics. A fully nonlinear extension of the concepts of absolute and convective instability introduced by Chomaz (Phys. Rev. Lett. 69 (1992) 1931) is recalled in connection with the broader problem of front and pattern selection. These new ideas are first illustrated on simple amplitude equations. Then the fully nonlinear concepts are applied to actual flows such as wakes and mixing layers. Furthermore, new scenarii involving secondary absolute instability are proposed and compared to the dynamics of the rotating disk and mixing layers experiment.

Expansion exponents for nonequilibrium systems

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of calculating the exponents are discussed. The principle of minimal expansion provides the basis for treating the problem of pattern selection. The exponents are also defined for stochastic dynamical systems. The analysis of the expansion-exponent behavior for quasi-isolated systems results in the formulation of two other principles: The principle of asymptotic expansion tells that the phase volumes of quasi-isolated systems expand at asymptotically large times. The principle of time irreversibility follows from the asymptotic phase expansion, since the direction of time arrow can be defined by the asymptotic expansion of phase volume.

Probabilistic approach to pattern selection

The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the probability distribution of patterns. Then the most probable pattern naturally corresponds to the largest probability weight. This approach provides the ordering principle for the multiplicity of solutions explaining why some of them are more preferable than others. The approach is applied to solving the problem of turbulent photon filamentation in resonant media.

Traveling-Wave Patterns in Binary Mixture Convection with Through Flow

The pattern selection problem in binary-mixture convection in an extended channel with a lateral through-flow is presented. The through-flow breaks left--right parity and changes pattern dynamics dramatically. The problem is studied based on computer simulation of the complete set of hydrodynamic equations (Oberbeck-Boussinesq approximation) in the two-dimensional rectangular channel with aspect ratio $\Gamma = 12$ and convection-suppressing lateral boundary conditions. A wide variety of new dynamical patterns is obtained, discussed and classified.

Two-frequency forced Faraday waves: weakly damped modes and pattern selection

Recent experiments [A. Kudrolli, B. Pier, J.P. Gollub, Physica D 123 (1998) 99–111] on two-frequency parametrically excited surface waves produced an intriguing “superlattice” wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves onset simultaneously, but with different spatial wave numbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure. Similar patterns have been shown to exist as primary solution branches of a generic 12-dimensional D 6 + ̇ T 2 -equivariant bifurcation problem, and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities [M. Silber, M.R.E. Proctor, Phys. Rev. Lett. 81 (1998) 2450–2453]. Here we use the spatial and temporal symmetries of the problem to argue that weakly damped harmonic waves may be critical to understanding the stabilization of this pattern in the Faraday system. We illustrate this mechanism by considering the equations developed by Zhang and Viñals [J. Fluid Mech. 336 (1997) 301–330] for small amplitude, weakly damped surface waves on a semi-infinite fluid layer. We compute the relevant nonlinear coefficients in the bifurcation equations describing the onset of patterns for excitation frequency ratios of 2 3 and 6 7 . For the 2 3 case, we show that there is a fundamental difference in the pattern selection problems for subharmonic and harmonic instabilities near the codimension-two point. Also, we find that the 6 7 case is significantly different from the 2 3 case due to the presence of additional weakly damped harmonic modes. These additional harmonic modes can result in a stabilization of the superpatterns.

Parametrically excited surface waves: two-frequency forcing, normal form symmetries, and pattern selection.

Motivated by experimental observations of exotic free surface standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the associated pattern-selection problem. With forcing frequency components in ratio m/n, where m and n are coprime integers that are not both odd, there is the possibility that both harmonic waves and subharmonic waves may lose stability simultaneously, each with a different wave number. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern-selection problem is greatly diminished in this situation. We verify our general bifurcation theoretic results within the example of one-dimensional surface wave solutions of the Zhang-Viñals model [J. Fluid Mech. 341, 225 (1997)] of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case that the forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Viñals. In sharp contrast, we find that when the forcing frequencies are in a ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially resonant bifurcating mode. This is consistent with the results of our general analysis.

On velocity and spacing selection in discontinuous precipitation—I. Simplified analytical approach

A new approach is proposed to the problem of pattern selection in discontinuous precipitation. It relies on the simultaneous calculation of growth velocities for both the precipitate lamellae and the interlamellar solid solution phase, and on the recognition that the processes of diffusional transport along grain boundaries and interphase boundaries are fundamentally different. The first is considered governed by lateral gradients of concentration, the second by gradients of curvature. It is shown that the simple hypotheses of thermodynamic equilibrium and diffusive flux continuity at the triple junction between the precipitate lamella and the initial and depleted parent phases (along with the requirement that the two phases grow at the same rate) is sufficient to remove the degeneracy of the problem; the new treatment provides a selection of spacing and transformation front velocity consistent with experimental results in the literature.

Snakes and corkscrews in core–annular down-flow of two fluids

Core–annular flow of two fluids is examined at the onset of a non-axisymmetric instability. This is a pattern selection problem: the bifurcating solutions are travelling waves and standing waves. The former travel in the azimuthal direction as well as the axial direction and would be observed as corkscrew waves. The standing waves travel in the axial direction but not in the azimuthal direction and appear as snakes. Weakly nonlinear interactions are studied to see whether one of these waves will be stable to small-amplitude perturbations. Sample situations for down-flow are discussed. The corkscrews tend to be preferred when the annulus is narrow, while snakes are more likely when the annulus is wide.

Long-wavelength thermal convection in a weak shear flow

The problem of thermal convection in an imposed shear flow is examined for a horizontal layer of fluid between poorly conducting boundaries. The horizontal scale H of the convective motion near its onset is much greater than the depth h of the fluid layer, with h/H being proportional to the one-fourth power of a Biot number appearing in the condition applied to the temperature at the horizontal boundaries. It is known that an asymptotic expansion in powers of h/H yields a nonlinear long-wavelength evolution equation for the depth-averaged temperature field that is spatially isotropic in the absence of an imposed shear flow, but is strongly anisotropic for 'strong' shear. We derive in this paper a nonlocal long-wavelength equation that bridges these two cases, and that contains each case in the zero-shear and large-shear limits. Using this evolution equation, we show how the shear flow stabilizes the longitudinal rolls to the zigzag instability, and how a preference for a square planform on a periodic square lattice gives way to a preference for longitudinal rolls near onset. The longitudinal rolls may then become unstable as the Rayleigh number is increased. The analytical work is illustrated by some numerical simulations of the full three-dimensional Boussinesq Navier-Stokes equations. The problem of pattern selection on a hexagonal lattice is also discussed, and some new results are presented.

Influence of boundaries on pattern selection in through-flow

The problem of pattern selection in absolutely unstable open flow systems is investigated by considering the example of Rayleigh-Bénard convection. The spatio-temporal structure of convection rolls propagating downstream in an externally imposed flow is determined for six different inlet/outlet boundary conditions. Results are obtained by numerical simulations of the Navier-Stokes equations and by comparison with the corresponding Ginzburg-Landau amplitude equation. A unique selection process is observed being a function of the control parameters and the boundary conditions but independent of history and system length. The problem can be formulated in terms of a nonlinear eigen/boundary value problem where the frequency of the propagating pattern is the eigenvalue.