Implicit Form Research Articles

Stability and modal evolution characteristics of pipe-in-pipe system with internal intermediate support

In this paper, the stability of the pipe-in-pipe (PIP) conveying fluid system with intermediate supports are studied. The focus of the study is mainly on the influence of the intermediate supports on the critical velocity boundary. The governing equations of the coupled system are established according to Hamilton’s principle, and the modal functions in analytical solution form and the frequency equation in implicit function form are obtained by using the Laplace transform technique. In the numerical discussion part, the influence of the stiffness and position of the support on frequencies, modal functions, and critical flow velocity of the system is discussed. In the stability region diagrams of the cantilever PIP system, it is found that when the position and stiffness of the support change, the minimum critical flow velocity is frequently converted between different modes, and there are two different types of critical flow velocity conversion phenomena (CFVC). And high-order flutter instability, ‘jump’ phenomenon, S-shaped critical velocity boundary and modal conversion phenomenon are discussed in detail. In addition, the effective and negative regions of the support in the cantilever PIP and simply supported PIP systems are given.

Synthesis of the neuro-fuzzy regulator with genetic algorithm

Real-acting objects are characterized by the presence of various types of random perturbations, which significantly reduce the quality of the control process, which determines the use of modern methods of intellectual technology to solve the problem of synthesis of control systems of structurally complex dynamic objects, allowing to compensate the influence of external factors with the properties of randomness and partial uncertainty. The article considers issues of synthesis of the automatic control system of dynamic objects by applying the theory of intelligent control. In this case, a neural network based on radial-basis functions is used at each discrete interval for neuro-fuzzy approximation of the control system, allowing real-time adjustment of the regulator parameters. The radial basis function is designed to approximate functions defined in the implicit form of pattern sets. The neuro-fuzzy regulator's parameter configuration is accomplished using a genetic algorithm, enabling more efficient computation to determine the regulator's set parameters. The regulator's parameters are represented as a vector, facilitating their application to multidimensional objects. To determine the optimal tuning parameters of the neuro-fuzzy regulator, characterized by high convergence and the possibility of determining global extrema, a genetic algorithm was used. The effectiveness of the neuro-fuzzy regulator is explained by the possibility of providing quality control of the dynamic object under random perturbations and uncertainty of input data.

Accuracy Examination of the Fourier Series Approximation for Almost Limiting Gravity Waves on Deep Water

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time.

An Explicit Scheme for Energy-Stable Simulation of Mass-Barrier Collisions with Contact Damping and Dry Friction

Collisions feature in the acoustics of many musical instruments, and as such need to be included in physical models that aim to capture the resulting dynamics. Previous studies have established various ways of constructing energy-stable schemes for numerical modelling of collisions, usually in implicit form. Recent methods use energy quadratisation in the derivation of explicit update forms, which are particularly useful in a real-time synthesis context. This approach is extended here by including contact damping and sliding friction in a 2D one-mass impact oscillator model, which serves as an initial testbed problem. The scheme’s guaranteed passivity is formally shown, and brief simulation and convergence results are included.

Long-term filtration of particles in a porous medium

The formation of grout sediment in the pores of loose rock increases the water resistance of the soil and strengthens the foundation. A one-dimensional model of filtration in a porous medium considers the particles transport by the flow of a carrier fluid and the deposition of particles on the framework of a porous medium. The purpose of the work is to study the concentrations of suspended and settled particles of a suspension over a long time. Exact and asymptotic methods are used to obtain a solution to the model. The exact solution is presented in an implicit integral form. A set of solutions in the form of traveling waves with an arbitrary initial condition and their asymptotics are constructed. For the exact solution, an explicit second-order asymptotic solution for a long time is obtained as an expansion in decreasing exponents. Comparison of the asymptotic solution with the traveling waves makes it possible to choose a single traveling wave corresponding to the exact solution. The closeness of the traveling wave to the exact solution of the filtration model is verified numerically. The traveling wave found determines the explicit asymptotics of the concentration of deposited particles for a long time.

Exploring weight bias and negative self-evaluation in patients with mood disorders: insights from the BodyTalk Project.

Negative body image and adverse body self-evaluation represent key psychological constructs within the realm of weight bias (WB), potentially intertwined with the negative self-evaluation characteristic of depressive symptomatology. Although WB encapsulates an implicit form of self-critical assessment, its exploration among people with mood disorders (MD) has been under-investigated. Our primary goal is to comprehensively assess both explicit and implicit WB, seeking to reveal specific dimensions that could interconnect with the symptoms of MDs. A cohort comprising 25 MD patients and 35 demographically matched healthy peers (with 83% female representation) participated in a series of tasks designed to evaluate the congruence between various computer-generated body representations and a spectrum of descriptive adjectives. Our analysis delved into multiple facets of body image evaluation, scrutinizing the associations between different body sizes and emotionally charged adjectives (e.g., active, apple-shaped, attractive). No discernible differences emerged concerning body dissatisfaction or the correspondence of different body sizes with varying adjectives. Interestingly, MD patients exhibited a markedly higher tendency to overestimate their body weight (p = 0.011). Explicit WB did not show significant variance between the two groups, but MD participants demonstrated a notable implicit WB within a specific weight rating task for BMI between 18.5 and 25 kg/m2 (p = 0.012). Despite the striking similarities in the assessment of participants' body weight, our investigation revealed an implicit WB among individuals grappling with MD. This bias potentially assumes a role in fostering self-directed negative evaluations, shedding light on a previously unexplored facet of the interplay between WB and mood disorders.

Post-Jubilee Reports of the Club of Rome: In Search of a Conceptual Strategy for Humanity’s Foreseeable Future

The article analyzes the reports of the Club of Rome issued subsequent to its semicentennial celebration. The analysis uncovers the evolutionary trajectory of the Club’s conceptual frameworks, transitioning from the stark alarmism prevalent in the early 1970s to a grounded optimism characteristic of the early 21st century. The majority of its publications, in explicit or implicit form, essentially respond to a question of Hamletian scale that arose within the discussions of the “limits to growth” model: Is it possible, and if so, how, to overcome the antagonism between the continuous growth of the needs of an increasing humanity and the relatively limited natural-resource potential of the biosphere? The analysis introduces an analysis of world development scenarios by 2050, ranging from inertial extrapolation of current trends to radical transformations of global political, socio-economic, and cultural processes. The discourse reflects on the report authors’ contemplations regarding societal adaptability to undergo a “true human revolution,” entailing a fundamental reassessment of established economic models and advancement toward innovative global governance strategies. The paper scrutinizes the assertion that society’s “unlearnability” is one of the key obstacles to the sustainable development of civilization. Significant emphasis is placed on the imperative for a comprehensive transformation encompassing the global educational landscape and the cultivation of a novel (sustainable) mindset, one that appreciates the intricate interplay among economic, environmental, and sociocultural perspectives on the global dynamics of the “humanity – biosphere – civilization” system. Humanity, overcoming the turbulences of contemporary world development, possesses all the prerequisites for a constructive analysis and design of strategic perspectives of the foreseeable future.

Amplitude of heat and mass transfer of gravity-driven convective oscillatory flow along inclined heated plate under reduced gravity and viscosity

As gravitation grows, the impact of interaction across two particles improves. The force of gravity is a critical process of transferring material along an angled surface. The main importance of present research is to generate wave oscillations in concentrating particles along an angled surface under weak gravitational pressure. Main goal of thermo-viscosity in current model is to produce maximum movement in concentrated particles for significant oscillating heat transport along buoyancy-based plate. The governing mathematical model is constructed for numerical and graphical outcomes of present mechanism under weak gravity and variable viscosity. To generate pertinent parameters, the model is changed into non-dimension form by using suitable variables. To observe oscillatory and amplitude sequence of results, the model is formulated into steady, real and imaginary equations. For programming sequence in FORTRAN tool, the primitive coefficients are used. The primitive based equations are solved by applying implicit form of finite difference method and Gaussian elimination scheme. The steady results such as fluid velocity, temperature variations and concentration profiles are observed for different physical factor under defined boundaries. The amplitude of oscillatory shear stress, oscillatory heat transport and oscillatory mass transport are explored by using steady results. It is noticed that the velocity of fluid enhances as viscosity decreases. It is found that the temperature variation grows as Schmidt number enhances but concentration profile decreases. It is observed that the prominent wave oscillations in heat transfer increases as Prandtl number enhances.

Classical Solution of the Second Mixed Problem for the Telegraph Equation with a Nonlinear Potential

For the telegraph equation with a nonlinear potential, we consider a mixed problem in the first quadrant in which the Cauchy conditions are specified on the spatial semiaxis and the Neumann condition is set on the temporal semiaxis. The solution is constructed by the method of characteristics in an implicit analytical form as a solution of some integral equations. The solvability of these equations is studied, as well as the dependence of the solutions on the smoothness of the initial data. For the problem under consideration, the uniqueness of the solution is proved and conditions are established under which a classical solution exists. If the matching conditions are not met, then a problem with conjugation conditions is constructed, and if the data is not smooth enough, then a mild solution is constructed.

Classical Solution of the First Mixed Problem for the Telegraph Equation with a Nonlinear Potential in a Curvilinear Quadrant

For the telegraph equation with a nonlinear potential in a curvilinear quadrant, we consider a mixed problem with the Cauchy conditions on a spatial half-line and the Dirichlet condition on a noncharacteristic curve. The solution of the problem is constructed by the method of characteristics in an implicit analytical form as a solution of integral equations. We study the solvability of these equations depending on the initial data and their smoothness. For the problem under consideration, the uniqueness of the solution is proved and conditions under which there exists a classical solution are established. A mild solution is constructed in the case of insufficiently smooth data of the problem.

Layered shallow water equations: Spatiotemporally varying layer ratios with specific adaptation to wet/dry interfaces

AbstractThe study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three‐dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter‐layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid‐scale eddy‐viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well‐balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test‐cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full‐scale model results in experimental scenarios at a lesser computational overhead.

The Security Jawbreaker

When someone stands at the front door of your home, what are the steps to let them in? If it is a member of the family, they use their house key, unlocking the door using the authority the key confers. For others, a knock at the door or doorbell ring prompts you to make a decision. Once in your home, different individuals have differing authority based on who they are. Family members have access to your whole home. A close friend can roam around unsupervised, with a high level of trust. An appliance repair person is someone you might supervise for the duration of the job to be done. For more sensitive locations in your home, you can lock a few doors, giving you further assurance. Making these decisions is an implicit form of evaluating risk tolerance, or your willingness to accept the chance that something might go against your best interests.

Learning Without Awareness by Academic and Nonacademic Samples: An Individual Differences Study

AbstractThis study addresses the role of awareness in learning and the variables that may facilitate adult second language (L2) implicit learning. We replicated Williams's (2005) study with a similar group of academic learners enrolled at university as well as a group of non‐college‐educated adults in order to explore the generalizability of the findings to an underrepresented population in research on L2 acquisition. Our results revealed that academic learners implicitly acquired items encountered during training (trained items), but this learning disappeared when academic and nonacademic groups were combined. We also observed modest correlations between intelligence and implicit learning of trained items; however, this association disappeared when other variables were considered. Overall, our study highlights the limited potential of implicit form–meaning associations for L2 adults in more general populations and emphasizes the challenges associated with convenience sampling in L2 research (Andringa & Godfroid, 2020). Additionally, it underscores the independence of individual differences in reading exposure, years of education, and nonverbal intelligence for implicit learning of trained items.

TrapezoidalNet: A new network architecture inspired from the numerical solution of ordinary differential equations

The architecture of deep neural networks is commonly determined via trial and error, resulting in inefficiency and a lack of architecture interpretability. Recent research shows that numerical solutions of ordinary differential equations have demonstrated great potential for designing network architectures. Implicit methods are generally more stable and accurate than explicit methods but are yet to be applied to neural network design. Unlike explicit methods that directly calculate the current state based on the previous state, implicit methods have to solve a nonlinear equation to get the approximate solution, which discourages using implicit methods in network design. In this paper, we propose replacing Euler's method with the trapezoidal rule, a scheme that is a second-order implicit method with much lower local truncation errors. The crux of our approach lies in first altering the trapezoidal rule from its implicit form to the explicit form and then designing the corresponding neural network. By introducing the multi-channel convolution and layer-sharing mechanism, we propose a new architecture called TrapezoidalNet. We expect TrapezoidalNet can outperform other deep neural networks based on explicit methods such as ResNet, FitResNet, FractalNet, and LM-ResNet on image recognition tasks. Experimental results on CIFAR10/100 datasets verify the effectiveness of TrapezoidalNet.

Adaptive Approximate Implicitization of Planar Parametric Curves via Asymmetric Gradient Constraints

Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, existing methods mostly suffer from the problems of maintaining geometric features and choosing a reasonable implicit degree. The present paper has two contributions. We first introduce a new regularization constraint (called the asymmetric gradient constraint) for both polynomial and non-polynomial curves, which efficiently possesses shape-preserving. We then propose two adaptive algorithms of approximate implicitization for polynomial and non-polynomial curves respectively, which find the “optimal” implicit degree based on the behavior of the asymmetric gradient constraint. More precisely, the idea is gradually increasing the implicit degree, until there is no obvious improvement in the asymmetric gradient loss of the outputs. Experimental results have shown the effectiveness and high quality of our proposed methods.

Mathematical Investigation to evoke the solar cell based parametric quantities from Implicit to Explicit form

The solar photovoltaic cell equivalence is of non-linear nature and it is more intricate to analyze. Henceforth, it is essential to explicate a mathematical based model in order to understand the non-linear dynamics of solar cell. To adjudicate the maximum power point, it is required to study and examine the composite characteristics by implementing iterative methods to perform mathematical computations. A mathematical canvas is needed to determine the values of series and shunt resistances present in solar cell. We can also compute different parasitic components of solar photovoltaic cell; fill factor analysis and also ideal factor calculations. Voltage equation is formulated in both 2-dimensional and 3-dimensional equation form. Mathematical based analysis has been performed and converted implicit form of equation to explicit based equation.

Asymptotic formula of Rayleigh wave speed in an orthotropic half-space coated by a thin piezoelectric film

ABSTRACT Piezoelectric thin films have been widely used in electro-acoustic devices including ones measuring Rayleigh wave speed. The main objective of this work is to find an explicit formula of Rayleigh speed taking into account the effect of the thin piezoelectric film. First the problem of Rayleigh surface waves propagating along an orthotropic substrate coated by a thin piezoelectric film is considered using Stroh’s formalism approach. Then, the exact secular equation of Rayleigh wave is obtained in implicit form. In case when the thickness of the thin layer is much smaller than the considering wavelength of Rayleigh waves, an asymptotic formula of Rayleigh speed is derived from the asymptotic form of the exact secular equation. The obtained asymptotic formula is simple enough and could be used in practice when Rayleigh speed is measured by using piezoelectric device. Numerical illustrations are carried out to show the validity of the obtained approximate formulas and its potential application in inverse problem.

Internal Gravity Waves from a Localized Source in Stratified Medium Flow with a Model Buoyancy Frequency Distribution

The problem of calculating internal gravity wave fields generated by a localized source in a stratified flow of finite thickness with a model buoyancy frequency distribution is considered. By using analytical representations of the buoyancy frequency, an implicit form of the dispersion relation is obtained, which depends on the Bessel functions of real index. Numerical results for dispersion curves, lines of equal phase, and wave amplitudes for various wave modes and stratified flow velocities are presented. The thickness of the stratified layer, the vertical gradient of the buoyancy frequency, and the magnitude of the flow velocity are the main factors affecting the amplitude-phase spatial transformation of the wave fields excited downstream.

Impacts of Exponentially Growing/Decaying Pressure Gradient on Mixed Convection Flow of Viscous Reactive Fluid in a Vertical Tube: A Numerical Approach

This study examined the effects of a pressure gradient that was exponentially increasing or decreasing on the mixed convection flow of viscous reactive fluids in a vertical tube between two concentric tubes with r = 0 and r = b. The nonlinear partial differential equation governing the flow formation are solved using the implicit finite difference form where all time differentials were calculated using the forward difference formula, and second order central differences were utilized to approximate the first and second derivatives. The impacts of several physical parameters, including shear stress, the rate of heat transfer, mixed convection, viscous reactive fluid parameter, activation energy, Prandtl number, and exponential decaying/growing pressure gradient on skin friction and Nusselt number were investigated. It's intriguing to see that raising the values of Frank–Kamenetskii (λ), mixed convection (Gre) as well as exponential growing pressure term increases the velocity fluid, However, in the case of exponential decay, the parameter drop also causes the fluid's velocity to diminish. The results also showed that a small bump in the viscous reactive fluid parameter considerably improves the energy profile.

Accelerated dynamics with dry friction via time scaling and averaging of doubly nonlinear evolution equations

In a Hilbert framework, for convex differentiable optimization, we analyze the long-time behavior of inertial dynamics with dry friction. In classical approaches based on asymptotically vanishing viscous damping (in accordance with Nesterov’s method), the results are expressed in terms of rapid convergence of the values of the function to its minimum value. On the other hand, dry friction induces convergence towards an approximate minimizer, typically the system stops at x when a given threshold ‖∇f(x)‖≤r is satisfied. We obtain rapid convergence results in this direction. In our approach, we start from a doubly nonlinear first-order evolution equation involving two potentials: one is the differentiable function f to be minimized, which acts on the state of the system via its gradient, and the other is the nonsmooth potential dry friction φ(x)=r‖x‖ which acts on the velocity vector via its sub-differential. To highlight the central role played by ∇f(x), we also deal with the dual formulation of these dynamics, which have a Riemannian gradient structure. We then rely on the general acceleration method recently developed by Attouch, Boţ and Nguyen, which consists in applying the method of time scaling and then averaging to a continuous differential equation of the first order in time. We thus obtain fast convergence results for second order time-evolution systems involving dry friction, asymptotically vanishing viscous damping, and Hessian-driven damping in the implicit form.