Smooth Case Research Articles

Pearcey universality at cusps of polygonal lozenge tilings

AbstractWe study uniformly random lozenge tilings of general simply connected polygons. Under a technical assumption that is presumably generic with respect to polygon shapes, we show that the local statistics around a cusp point of the arctic curve converge to the Pearcey process. This verifies the widely predicted universality of edge statistics in the cusp case. Together with the smooth and tangent cases proved by Aggarwal‐Huang and Aggarwal‐Gorin, these are believed to be the three types of edge statistics that can arise in a generic polygon. Our proof is via a local coupling of the random tiling with nonintersecting Bernoulli random walks (NBRW). To leverage this coupling, we establish an optimal concentration estimate for the tiling height function around the cusp. As another step and also a result of potential independent interest, we show that the local statistics of NBRW around a cusp converge to the Pearcey process when the initial configuration consists of two parts with proper density growth, via careful asymptotic analysis of the determinantal formulas.

Towards Stability and Generalization Bounds in Decentralized Minibatch Stochastic Gradient Descent

Decentralized Stochastic Gradient Descent (D-SGD) represents an efficient communication approach tailored for mastering insights from vast, distributed datasets. Inspired by parallel optimization paradigms, the incorporation of minibatch serves to diminish variance, consequently expediting the optimization process. Nevertheless, as per our current understanding, the existing literature has not thoroughly explored the learning theory foundation of Decentralized Minibatch Stochastic Gradient Descent (DM-SGD). In this paper, we try to address this theoretical gap by investigating the generalization properties of DM-SGD. We establish the sharper generalization bounds for the DM-SGD algorithm with replacement (without replacement) on (non)convex and (non)smooth cases. Moreover, our results consistently recover to the results of Centralized Stochastic Gradient Descent (C-SGD). In addition, we derive generalization analysis for Zero-Order (ZO) version of DM-SGD.

Inexact direct-search methods for bilevel optimization problems

In this work, we introduce new direct-search schemes for the solution of bilevel optimization (BO) problems. Our methods rely on a fixed accuracy blackbox oracle for the lower-level problem, and deal both with smooth and potentially nonsmooth true objectives. We thus analyze for the first time in the literature direct-search schemes in these settings, giving convergence guarantees to approximate stationary points, as well as complexity bounds in the smooth case. We also propose the first adaptation of mesh adaptive direct-search schemes for BO. Some preliminary numerical results on a standard set of bilevel optimization problems show the effectiveness of our new approaches.

The Influence Of Profitability And Financial Leverage On Earnings Management And Its Impact On The Value Of Manufacturing Companies In The Indonesian Stock Ex-change (Case Study Of The Automotive Sub-Sector Period 2018-2022)

The practice of income smoothing still occurs in the Indonesian economy. There are sever-al cases of income smoothing that have occurred, including at PT. Kimia Farma Tbk, PT and Lippo Tbk where these companies have published different financial reports. The purpose of this research is to determine the direct effect of profitability on income smoothing, fi-nancial leverage on income smoothing, profitability on company value, financial leverage on company value, the indirect effect of profitability on company value through income smoothing, financial leverage on company value through income smoothing and Income smoothing has a direct effect on company value. This research uses a mixed method. The population used in this research is automotive sub-sector manufacturing companies listed on the Indonesia Stock Exchange for the 2018-2022 period. The sampling method is to use a purposive sampling technique so that the samples obtained are 50 samples. The re-search results show that there is no direct influence of profitability on income smoothing, there is no direct influence of financial leverage on profit smoothing, there is a direct influ-ence of profitability on firm value, there is no direct influence of financial leverage on firm value, there is no indirect influence income smoothing between profitability and company value, there is no indirect effect of income smoothing between financial leverage on com-pany value and there is no direct effect of income smoothing on company value.

Roll waves in a predictive model for open-channel flows in the smooth turbulent case

A depth-averaged model for turbulent open-channel flows with breaking roll waves on a sloping smooth bottom is derived under an assumption of independence between the wall turbulence and the roller turbulence. The model includes four variables – the water depth, the average velocity, and two variables called enstrophy, the shear enstrophy and the roller enstrophy – which take into account the deviations of the velocity with respect to its depth-averaged value due to shear effect and roller turbulence, respectively. The four equations of the model are the mass, momentum, energy and shear enstrophy balance equations, with the mathematical structure of the Euler equations of compressible fluids, with an additional transport equation and with source terms. The system is hyperbolic. The roller enstrophy is created by shocks. A non-zero value of the roller enstrophy indicates a breaking wave and a turbulent roller. The model is solved by a fast and well-known numerical scheme, with an explicit finite-volume method in one step. The model is used to simulate periodic and natural roll waves with a good agreement with existing experimental results. There is no parameter to calibrate in the model, which gives it a predictive character.

Multiobjective optimization of Vortex Generators for heat transfer enhancement in turbulent flows

Convective heat transfer can be enhanced by streamwise vortices and coherent flow structures produced downstream Vortex Generators (VGs). The thermal performance depends on the VG shape which controls the intensity and topology of the vortices. Thus, VG shape optimization is a major challenge in designing sustainable and efficient heat exchangers. In the present study, a multi-objective optimization is performed through large space exploration design to find optimal VG shapes that adapt to different flow regimes. Simulations are carried out in parallel plate turbulent flow for three different Reynolds numbers; Re1=4600,Re2=9920, and Re3=30050. The present numerical results are first validated against numerical and experimental data from the open literature. Then, and for the first time, seven design parameters are investigated, based on VG shape dimensions. The new optimized VG show a thermal enhancement factor between 11 and 35%, relative to a smooth channel case, and between 3 and 14%, relative to different VG shapes from the recent open literature. The present results are analyzed in details by focusing on the physics of the flow structure and its correlation to the convective heat transfer enhancement using local criteria for flow visualization and vortex intensity quantification.

Roughness effects on compressible turbulent boundary layers under different Mach numbers and wall temperature conditions

Compressible turbulent boundary layers over a zero-pressure gradient flat plate with three-dimensional sinusoidal roughness are simulated by direct numerical simulation. The roughness effects on surface drag, velocity transformation, and turbulence fluctuation characteristics are analyzed in a wide range of Mach numbers (Ma∞ = 2.25–7.25) and different ratios of wall-to-recovery temperature (Tw/Taw = 0.43 and 0.84) conditions. It is found that the roughness significantly amplifies the surface drag coefficient due to the extra pressure drag induced by roughness, and the relative increase in surface drag induced by the roughness rises by 31.1% when Ma∞ changes from 2.25 to 7.25. Current compressible velocity transformations cannot make the logarithmic region of velocity profiles independent of Tw/Taw conditions for rough cases due to the strong wall heat transfer effect below roughness peak. Therefore, a new velocity transformation (Uρt+) is proposed to make the logarithmic region of Uρt+ profiles and roughness induced a downward shift of Uρt+ profiles (ΔUρt+) in a logarithmic region independent of Ma∞ and Tw/Taw conditions. Further numerical experiments validate that, in hypersonic boundary layers, the relation between ΔUρt+ and equivalent sand-grain roughness height Reynolds number still satisfies the roughness function proposed earlier for incompressible flows. Moreover, roughness significantly changes the distribution of mean turbulent kinetic energy (TKE) in compressible turbulent boundary layers: TKE is suppressed at the bottom of roughness, while reaching its maximum at the roughness peak, which is 50%–60% larger than that in smooth case. Finally, the expansion/compression wave patterns induced by roughness alter the turbulence fluctuations in outer layer.

Amplitude modulation in turbulent boundary layer over anisotropic porous wall

In this study, the amplitude modulation effect in a turbulent boundary layer over anisotropic porous walls is investigated experimentally at the Reynolds number based on friction velocity of Reτ = 236–319. The streamwise and wall-normal velocity fields were measured using time-resolved particle image velocimetry. To clarify the coherent structures related to the amplitude modulation over the porous wall with skin friction reduction effect, the large-scale structures are extracted from the low-pass filtered streamwise velocity fluctuations. The small-scale events related to high fluctuation energy are detected by the variable-interval space-averaging technique. Over the porous wall, the induced upwash and downwash motion leads to a notable suppression of large-scale structures. The small-scale motions in the near-wall region are mainly caused by the ejection events, while the sweep events are significantly suppressed. The amplitude modulation effects indicate that the positive and negative large-scale velocity streaks produce suppression and enhancement effects to the near-wall small-scale turbulence, respectively, which is contrary to the conventional phenomenon over the smooth wall case. The interaction between outer large-scale and inner small-scale structures is significantly weakened by the porous wall, contributing to the overall skin friction reduction.

A note on polarized varieties with high nef value

Abstract We study the classification problem for polarized varieties with high nef value. We give a complete list of isomorphism classes for normal polarized varieties with high nef value. This generalizes classical work on the smooth case by Fujita, Beltrametti and Sommese. As a consequence we obtain that polarized varieties with slc singularities and high nef value are birationally equivalent to projective bundles over nodal curves.

RATE-ADAPTIVE BOOTSTRAP FOR POSSIBLY MISSPECIFIED GMM

We consider inference for possibly misspecified GMM models based on possibly nonsmooth moment conditions. While it is well known that misspecified GMM estimators with smooth moments remain $\sqrt {n}$ consistent and asymptotically normal, globally misspecified nonsmooth GMM estimators are $n^{1/3}$ consistent when either the weighting matrix is fixed or when the weighting matrix is estimated at the $n^{1/3}$ rate or faster. Because the estimator’s nonstandard asymptotic distribution cannot be consistently estimated using the standard bootstrap, we propose an alternative rate-adaptive bootstrap procedure that consistently estimates the asymptotic distribution regardless of whether the GMM estimator is smooth or nonsmooth, correctly or incorrectly specified. Monte Carlo simulations for the smooth and nonsmooth cases confirm that our rate-adaptive bootstrap confidence intervals exhibit empirical coverage close to the nominal level.

Self-covering, finiteness, and fibering over a circle

A topological space is called self-covering if it is a nontrivial cover of itself. We prove that a closed self-covering manifold M M with free abelian fundamental group fibers over a circle under mild assumptions. In particular, we give a complete answer to the question whether a self-covering manifold with fundamental group Z \mathbb Z is a fiber bundle over S 1 S^1 , except for the 4 4 -dimensional smooth case. As an algebraic Hilfssatz, we develop a criterion for finite generation of modules over a commutative Noetherian ring. We also construct examples of self-covering manifolds with nonfree abelian fundamental group, which are not fiber bundles over S 1 S^1 .

On a Frank-Wolfe approach for abs-smooth functions

We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as ℓ 1 regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose a generalization to the traditional Frank-Wolfe gap and prove that first-order minimality is achieved when it vanishes. We derive a convergence rate for our algorithm which is identical to the smooth case. Although our algorithm necessitates the solution of a subproblem which is more challenging than the smooth case, we provide an efficient numerical method for its partial solution, and we identify several applications where our approach fully solves the subproblem. Numerical and theoretical convergence is demonstrated, yielding several conjectures.

Orlov's Theorem in the smooth proper case

We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier–Mukai transforms to the case when those varieties are smooth and proper.

TURNING REGION HEAT TRANSFER IN FIVE, STATIONARY AND ROTATING, MULTI-PASS CHANNELS WITH VARIOUS ASPECT RATIOS

Abstract This work summarizes studies that experimentally investigated the effect of rotation on heat transfer in the 180-deg tip and hub turns of cooling channels with various aspect ratios (ARs). The studied AR ranges from 1:4 to 4:1, which is the typical range within turbine blades. In addition to the smooth surface case, the cases with 45-deg angled ribs and turning vanes are also included. For several designs, the effect of channel orientation with respect to the angle of rotation is also investigated. This work covers a wide range of Reynolds and buoyancy numbers. The rib turbulators are found to have higher heat transfer enhancement and larger disturbance on the flow impingement on the tip and hub walls in channels with a wider aspect ratio. The rotational effect is reduced by the presence of ribs and turning vanes, and it is also reduced in the blade-shaped channels with the angled rotation feature. The tip wall heat transfer is increased by rotation due to the pumping effect from the centrifugal force; however, the hub wall heat transfer is reduced. The effect of rotation is most prominent in the first pass of the channels and is gradually mitigated in the following pass after the turns. This work provides stationary and rotational heat transfer coefficients in the tip and hub turning regions in blades, and heat transfer correlations for a variety of cooling channel designs can be generated, which is of benefit to the gas turbine community.

Fast-slow dynamics analysis in an externally excited smooth and discontinuous oscillator with a pair of irrational nonlinearities

The study of fast-slow oscillations in systems with irrational nonlinearity that may yield abundant dynamical mechanisms is not well developed. This paper aims to investigate the fast-slow dynamics in an excited mass-spring oscillator with a pair of irrational nonlinearities, which can undergo the dynamical transition from smooth to discontinuous characteristics depending on the values of a smoothness parameter. Three different types of fast-slow oscillations are reported in this interesting smooth and discontinuous (SD) oscillator with a pair of irrational nonlinearities. Due to the smooth and discontinuous characteristics of this SD oscillator, we consider its dynamical behaviors under the smooth and discontinuous cases, respectively. Based on the fast-slow analysis and the two-parameter bifurcation analysis, the smooth fast-slow dynamics associated with fold hysteresis and its turnover are revealed. In the discontinuous case, the system can be viewed as a piecewise-smooth dynamical system governed by three different subsystems in different regions divided by two nonsmooth boundaries. In particular, the nonsmooth boundaries can be divided into parts with different dynamical behaviors, including escaping and crossing lines. Unlike the smooth case, there is no change in the stability of the equilibrium in these three subsystems. However, transitions of system trajectory induced by crossing lines can account for the generation of fast-slow oscillations in the piecewise-smooth system. As a result, the smooth and piecewise-smooth fast-slow dynamics in the excited SD oscillator with a pair of irrational nonlinearities are revealed, which deepens the understanding of fast-slow dynamics of the dynamical systems with irrational nonlinearity.

Hydrothermal and entropy generation performance of convergent tubes with various dimple shapes

This paper introduces a comprehensive study on the hydrothermal and entropy generation performance of convergent tubes designed with different dimple shapes. The effects of the dimple shape on the flow characteristics (heat transfer and friction) are investigated using validated computational fluid dynamics (CFD) numerical modelling and simulation tools. Inside convergent tubes with different dimple designs, turbulent flows are subjected to a continuous heat flux of 40 kW/m2. Dimpled tube geometries of different diameter ratios (DR) were built within ANSYS-Fluent software (V2022 R2). Four different dimple shapes were investigated: (a) spherical, (b) cylindrical, (c) conical, and (d) stepped-conical. These dimple shapes were examined to investigate the optimal configuration with the best hydrothermal and entropy generation performance. A comparison is made against the baseline straight smooth tube case. The main performance indicators for comparison are Nusselt number (Nu), friction factor (f), and thermal enhancement factor (TEF), calculated for different Reynolds numbers, Re = 3000 to 40,000, and at different diameter ratios, DR = 1 to 2. In addition, thermal, viscous, and total entropy components, the Bejan number (Be), the enhanced entropy generation ratio (Ns,en), and the irreversibility distribution ratio (φs) are evaluated based on the selected geometrical configurations. The results showed that the dimple shape significantly affects the hydrothermal and entropy generation characteristics of convergent tubes. The best average value of the TEF was attained by convergent tubes with stepped-conical dimple shapes at DR = 1.75, which represents a 7.81% increase over the reference smooth tube (the maximum TEF value is 1.3243 at Re = 3000 and DR = 1.25). Furthermore, the minimum levels of Ns,en were achieved by tubes with stepped-conical dimples, with average reductions of 36.92% over the studied Re range. The study provides valuable insights into the design and optimization of convergent tubes with various dimple shapes for various applications.

Direct numerical simulations of the drag degradation mechanism in channel flow over trapezoidal riblets

Direct numerical simulations of turbulent channel flows with trapezoidal riblets were conducted to analyze the characteristics of the near-wall flow structures in the drag reduction, drag neutral, and drag increase regimes. The trapezoidal riblets possess a tip angle of α =15°and a height–to-width ratio of k/s = 0.335 for cross-section-area based sizes lg+=Ag+= 11.7, 17, 23.2, and 29 at a friction Reynolds number of Reτ=395. The Reynolds stresses are compared with the smooth wall case, and it is observed that the intensity of the turbulent activities in the boundary layer is diminished for drag reduction riblet and enhanced for drag increase riblets. The roughness sublayer indicates that riblet only directly affect the near-wall region of the flow. By applying the Fukagata, Iwamoto, and Kasagi (FIK) identity in Phys. Fluids, vol. 14, 2002, L73, it is found that the modification of the overall drag is mainly due to the turbulent shear stress. The variation of the dispersive stress is only evident within the roughness sublayer for the drag increasing riblets. The enhanced mean wall-shear stress in the valley is responsible for the drag increase for oversized riblets. The production and convection terms of the turbulent stress reveal that although the total drag contribution is trivial, the convection inside the riblet valleys caused by secondary flow is crucial for the redistribution of the turbulent stress and drag increase of oversized riblets.

Flow characteristics and passive flow control of circular cylinders with triangular vortex generators: An experimental investigation

Optimizing flow patterns around cylinders is crucial for diverse engineering applications, aiming to mitigate vibrations induced by vortex shedding and minimize drag. Strategies, such as the implementation of vortex generators and modifications in the cylinder's surface geometry, are explored to optimize flow patterns and enhance the performance of structures exposed to fluid dynamics. This study investigated the flow characteristics of a smooth circular cylinder and cylinders equipped with triangular vortex generators placed at different position angles (α=15°, 30°, 60°, and 75°) and yaw angles (β=30°, 45°, 60°, and 75°) at the surface. The particle image velocimetry technique is used to measure the instantaneous and time-averaged velocities of the fluid flow over cylinders at Reynolds Number 8000. It is found that flow characteristics are highly dependent on the position angle of the triangular vortex generators. Specifically, at α=30° and β=60°, a substantial reduction of 17.3, 10.3, and 19.5 % occurred in normalized streamwise and root mean square of cross-stream velocity fluctuations and turbulent kinetic energy values, respectively, in comparison to that of the smooth circular cylinder. Furthermore, a noteworthy drag reduction of 33.3 % was achieved in the case of α=30° and β=60° through the elongation of the recirculation length and the establishment of a low-pressure zone away from the base of the circular cylinder. On the other hand, the lowest Strouhal number is obtained as 0.180 in the case of α=75° and β=30° where it was 0.211 at the smooth CC case. As a result, triangular vortex generators with an area of 1.1% of the total side projection area of the cylinder were found to be very effective in flow control.

Chaotic behaviors and coexisting homoclinic cycles in a class of 3D piecewise systems

Investigating homoclinic trajectories and chaotic behaviors, is conducive to better understanding the fourteenth problem listed by Smale in his response to Arnold. This paper analytically detects coexisting homoclinic cycles without symmetry required in a class of three-dimensional (3D) piecewise systems, which is significantly different from the smooth case where a pair of homoclinic cycles with respect to one equilibrium point are generally symmetric. Moreover, it is rigorously shown that such coexisting cycles gives rise to chaos by means of analyzing a Poincaré map. An example finally is presented to illustrate the proposed results.

Combined effect of magneto hydrodynamics, couple stress, and viscosity variation on squeeze film characteristics of a cylinder and rough flat plate

The present research theoretically analyzes the impact of magnetohydrodynamics (MHD) and viscosity variation on couple stress squeeze film properties of a cylinder and a rough planar surface. The generalized stochastic Reynolds flow equation is derived by utilizing Stokes flow theory and Christensen's stochastic flow model. The solutions for pressure, load-carrying capability, and squeeze film time for longitudinal and transverse roughness patterns are derived and illustrated graphically to examine the impacts of MHD, couple stress, and viscosity variation factors. The results reveal that, in comparison with the smooth case, the one-dimensional longitudinal (transverse) roughness pattern decreases (enhances) the pressure, squeeze film time, and load-carrying capability. The numerical comparative results between Sreekala et al. (Lect Notes Electr Eng 928:765–774, 2023) analysis and the current analysis are performed and found excellent agreement.