Singular Force Research Articles

Modulation of optical force by adjusting the distance between three-layer photonic crystal slabs

Optical forces induced by polarization singularities from photonic crystal slabs (PCSs) have gained widely attention in recent years. To enhance the degree of freedom in controlling far-field optical forces, we propose and design a three-layer PCSs structure that simultaneously possesses multiple optical forces with reconfigurability. By modulating the interlayer spacing, the coupling strength between the slabs is regulated, resulting in a band transition from the nodal rings to the nodal ridge, which facilitates the generation of dual polarization vortices. These dual polarization vortices induce multiple phase singularities at their boundaries, leading to multiple optical force singularities, offering the possibility of capturing and dispersing nanoparticles. Interestingly, tuning the spacing among the slabs can transform the converging force into the diverging force at the center, therefore achieving particle screening. This work not only expands the application of nodal ridges to optical force in photonic structures but also provides a feasible approach for the generation of double-ring vortex beam in the nano-optics field.

A Chain Scission-Induced Anisotropic Damage Constitutive Model for Double Network Hydrogels

This work develops a chain scission-induced anisotropic damage constitutive model for double network (DN) hydrogels while considering the damage cross effect. A free energy of a single polymer chain comprising the configuration entropy of the polymer chain and the internal energy of persistent segments is proposed to avoid the force singularity caused by chain stretch limit. Then, a distribution function of the initial stretch ratio of polymer chains in DN hydrogels is derived to consider the randomness of chain length. Based on the micro-sphere full-network model and an energy-form fracture criterion of polymer chains, the damage evolution model of polymer chains in a certain orientation is formulated by the critical initial stretch ratio of the polymer chain, showing that only polymer chains with the initial stretch ratio lower than the critical initial stretch ratio survive in a certain chain stretch. The critical initial stretch ratio is determined by the maximum chain stretch and the maximum first invariant of the deformation state by considering the damage cross effect. Using the developed damage constitutive model, we describe the stress softening, strain hardening behavior and the nonmonotonic stress–strain curve of DN hydrogels. It also reveals that the residual strain of DN hydrogels in the loading cycles is caused by the anisotropic damage of polymer chains in DN hydrogels.

Internal sites of actuation and activation in thin elastic films and membranes of finite thickness.

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon externally imposed deformations. We theoretically analyze the geometry of isotropic, flat, thin, linearly elastic films or membranes of finite thickness, laterally extended to infinity. At the mathematical core of such characterizations are the fundamental solutions for localized force and stress singularities associated with corresponding Green's functions. We derive such solutions in three dimensions and place them into the context of previous two-dimensional calculations. To this end, we consider both no-slip and stress-free conditions at the top and/or bottom surfaces. We provide an understanding for why the fully free-standing thin elastic membrane leads to diverging solutions in most geometries and compare these situations to the truly two-dimensional case. A no-slip support of at least one of the surfaces stabilizes the solution, which illustrates that the divergences in the fully free-standing case are connected to global deformations. Within the aforementioned framework, our results are important for associated theoretical characterizations of thin elastic films, whether supported or free-standing, and of membranes subject to internal or external forces or stresses.

Constitutionalizing in the Anthropocene

The Anthropocene thesis, in its rejection of both the modernist separation between ‘humans’ and ‘nonhumans’ as well as in its treatment of ‘humans’ as a singular global geophysical force, presents fundamental challenges to constitutional theory and practice. First, in terms of conceptual and foundational transformations, the Anthropocene provokes the reconceptualization of legal relations as never being limited to human concerns, but as always and already part of more-than-human collectives. These legal relations are organized by the co-agency of humans and nonhumans, in recognition of shared vulnerabilities and in relations premised on care. This reconceptualization demands a new understanding of representational practices that could constitutionalize more-than-human relations as political and legal collectives. Second, emergent technologies such as genetic and climate engineering introduce fundamental questions about regulatory modalities available in the Anthropocene, and the role that law plays in this regard. Such technologies have given rise to the possibility of ‘ruling by design’, by technologically mediating ‘natural’ forces or Earth system processes to achieve pre-established regulatory goals. This possibility raises critical concerns about the remaining role for law in legitimising and enabling such developments. Finally, the temporal dimensions of the Anthropocene thesis cast a critical light on law’s potential for driving radical transformations in (un)governance. In imagining future legal architectures capable of manifesting more-than-human constitutionalism, it is necessary to excavate the historical role that foundational legal principles and institutions – such as sovereignty and personhood – have had in facilitating exploitative relations between and beyond humans.

Learning the effective adhesive properties of heterogeneous substrates

Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a heterogeneous substrate. There has been recent interest in the use of machine learning in multiscale modeling where macroscale constitutive relations are learnt from data gathered from repeated solution of the microscale problem. We extend this approach to peeling; this is challenging because peeling from heterogeneous substrates is characterized by pinning where the peel front gets stuck at a heterogeneity followed by an abrupt depinning. This results in a heterogeneity dependent critical force and a singular peel force vs. overall peel rate relationship. We propose a neural architecture that is able to accurately predict both the critical peel force and the singular nature of the peel force vs. overall peel rate relationship from the heterogeneous adhesive pattern. Similar issues arise in other free boundary and free discontinuity problems, and the methods we develop are applicable in those contexts.

From BGK-alignment model to the pressured Euler-alignment system with singular communication weights

This paper is devoted to a rigorous derivation of the isentropic Euler-alignment system with singular communication weights ϕα(x)=|x|−α for some α>0. We consider a kinetic BGK-alignment model consisting of a kinetic BGK-type equation with a singular Cucker-Smale alignment force. By taking into account a small relaxation parameter, which corresponds to the asymptotic regime of a strong effect from the BGK operator, we quantitatively derive the isentropic Euler-alignment system with pressure p(ρ)=ργ, γ=1+2d from that kinetic equation.

George Miller’s “old-fashioned Hollywood studio”: corporate authorship at Kennedy Miller, 1981–1991

ABSTRACT Australia’s George Miller, director of the Mad Max films and others, has an international reputation as a singular creative force. But this reputation overlooks key facts about Miller’s career and working methods, including his co-founding and stewardship of the production company Kennedy Miller (now Kennedy Miller Mitchell), which organized production along collaborative and collective lines. In this article, I undertake an organizational analysis of Kennedy Miller from 1981 to 1991, the period that led Australian film scholars to describe the firm as akin to a classical Hollywood studio operation. I argue that just as we recognize classical Hollywood studios as possessing a collective ‘genius’ that delimits individual claims to authorship, so should we understand Kennedy Miller in this period as possessing a corporate authorship over its film and television production. I locate this strong ‘house’ identity in the firm’s organizational structure, its distinctive culture of ‘comprehensivism’, its collaborative creative procedures, and in the discourses of publicity and critical reception that surrounded its output. I conclude by contending that this understanding of Kennedy Miller’s corporate authorship requires that we reframe our understanding of Miller’s practice to account for his role in this collaborative structure.

Minimum Friction Coefficient-Based Precision Manipulation Workspace Analysis of the Three-Fingered Metamorphic Hand

Abstract Reconfigurable robotic hands can constitute one of the future trends of dexterous manipulator design, as they can strike a balance between precision, force exertion, flexibility, and adaptability. However, the feasible manipulation workspace of a reconfigurable robotic hand, the metamorphic hand, is complex as the finger operation planes alter with the reconfigurable palm’s motions. Different useful workspace approaches and grasp quality metrics have been introduced, but a precision manipulation workspace (PMW) approach for reconfigurable robotic hands has yet to be presented. This paper presents a hand workspace taxonomy based on previous studies, and a new approach to obtaining a PMW of a robotic hand which satisfies three properties: force closure, singularity avoidance, and interference avoidance. A grasp quality metric, termed the minimum friction coefficient (MFC), is introduced to indicate the force-closure conditions of a robotic hand’s configurations. Unlike the previous grasp quality metrics targeting online grasp-planning tasks, this MFC-based measure focuses on the offline design of robotic hands. This method is essential for conducting grasp planning, design optimization, and actuation reduction for reconfigurable robotic hands. Further, the approach is applied to a three-fingered metamorphic hand, and the results are studied thoroughly.

Unfitted finite element methods based on correction functions for Stokes flows with singular forces of low regularity

This paper presents an unfitted finite element method based on correction functions for solving stationary Stokes flows with singular forces acting on an immersed interface. It has been shown that the singular force is equivalent to a nonhomogeneous jump condition on the interface. In this paper, we consider the case that the jump has a low regularity so that it is impossible to use pointwise values on the interface to construct correction functions, as done in Guzmán et al. (2016). The natural way to deal with the problem is to use mean values of the jump on the parts of the interface cut by elements, instead of using pointwise values. However, we show that it may cause instability and the constant in the error estimate may depend on the interface location relative to the mesh. Inspired by Guo et al. (2019), we use a larger fictitious circle to overcome these issues. Associated with the correction functions, we consider two stable finite element pairs: the Mini element and the P2−P0 element, including the cases of continuous and discontinuous pressures. The optimal approximation capabilities of the correction functions and optimal error estimates of the finite element methods are both derived with a hidden constant independent of the interface location relative to the mesh. Numerical examples are provided to validate the theoretical results.

Stability of Navier–Stokes System with Singular External Force in Fourier–Herz Space

Stability of Navier–Stokes System with Singular External Force in Fourier–Herz Space

Disruption, interrupted

This article investigates how the dual demands of finance and social impact affect the relationships of founders to disruption, as a rhetorical function, material goal and relational context. Building on recent studies of innovation and entrepreneurship such as Bardinelli (2019), Irani (2019) and Lindtner (2020), the article offers a nuanced view of disruption that complicates unidimensional narratives of financialization as a singular force and accounts for the complexity of reconciling financial and social interests. Based on data gathered at a startup participating in a government-funded accelerator program in Melbourne, Australia, we analyse how the logics of finance impact entrepreneurial experience in an early-stage social enterprise startup. Our data suggests that, in their attempts to attract the attention and funding of financial investors, founders of early-stage startups focus more on proving the value of their disruption in a rhetorical sense than on refining the materially disruptive potential of their products to ensure real world social impact. By analysing disruption through a relational lens, we identify four layers of disruption (product innovation; social value; financial return; and labour relations) to which early-stage startups are aligned, and through which their products and personal lives are transformed.

Gaining two derivatives on a singular force in the 2D Navier-Stokes equations

It has long been known, for the autonomous 2D Navier-Stokes equations with singular forcing in H−1, that there exists a unique solution, globally bounded in L2, i.e., with a gain of one derivative on the force in terms of regularity. These classical techniques also show us that the solution is almost everywhere in H1. On the other hand, if the forcing term is in L2, it is known that the solution is bounded in H2 globally – a gain of two derivatives. In this paper we prove new maximal regularity results for the 2D Navier-Stokes equations. First, we explore classical techniques to show that if the force is in Hα for α∈(−1,0), then the solution gains two derivatives globally. These methods break down for forces in H−1. In this scenario, we use the Littlewood-Paley decomposition in Fourier space, and an appropriate frequency splitting, to show that for any initial data in H1 there exists a bounded in H1 solutions for a short time interval.

In dialogue with nails: Kuzgun Acar’s Elegy to a Modern Man

Little research has been published on the work of Ethiopian-Turkish sculptor and political activist Kuzgun Acar (1928–1976), whose prolific artistic practice constitutes a prescient material inquiry at the intersection of class, blackness and postcolonial identity. His work Elegy to a Modern Man, made entirely from nails, was awarded the first prize at the second Biennale de Paris in 1961. This paper will examine how Elegy to a Modern Man interacts with, and departs from, the use and signification of nails as material and motif in modern and pre-modern art practices. Discussing the genealogical relationships between artworks employing nails either as their primary artistic medium or as the bearers of symbolic meaning, I will trace how Elegy to a Modern Man draws on and dissents from early deployments of nails, including their use in Christian allegory. I will also explore how Acar's work relates to, and differentiates from, the materiality and signification of nails in Man Ray's Le Cadeau (1921) and Congolese Nkisi figures. By examining Kuzgun Acar's work, this paper aims to subvert the common assumption that formal and conceptual innovations in the visual arts originate from a putative ‘center’ and are appropriated or copied by artists working in the so-called peripheries. I challenge these assumptions by arguing that an understanding of Kuzgun Acar's practice, as part of a broader map of artistic practices and influences without denying the singular force of his innovation, allows us to reassess the role played by artists outside of the metropolitan centers of the art world in producing and shaping the contemporary languages and forms of art. This article will do so by employing a transnational comparative approach, finding in a variety of approaches across time, space, and culture, the context within which the continuities and departures at play in Acar's work can be understood.

A singular inter-particle force in Cucker-Smale model to avoid collisions

In this paper, by introducing a singular inter-particle force into Cucker-Smale model, the result of collision-avoidance is obtained. The inter-particle force can switch between attractive and repelling with the change of the inner product of relative velocities and positions, which is different from the force repelling only and more in line with the internal binding force of multi-agent systems. Through the establishing of Lyapunov functions, we show that the system can avoid collisions when initial positions are non-collisional. Moreover, for Cucker-Smale model with the singular inter-particle force, results about flocking behaviour are presented.

Exact solution for the response of an arbitrarily-curved beam subject to a moving load

An arbitrarily curved beam under the effect of a moving load has been considered. An analytical series solution has been developed for the case when the beam cross-section is symmetrical so that it resides in a plane during the motion. The moving force is assumed to be a singular force sliding through the length of the beam with constant speed while its direction always pointing in the principal normal of the curved shape of the beam. After developing the general solution for any plane beam, example computations were carried out on a specific example by means of power series expansion.

A Level Set Method for the Simulation of Moving Contact Lines in Three Dimensions

We propose an efficient numerical method for the simulation of multi-phase flows with moving contact lines in three dimensions. The mathematical model consists of the incompressible Navier-Stokes equations for the two immiscible fluids with the standard interface conditions, the Navier slip condition along the solid wall, and a contact angle condition which relates the dynamic contact angle to the normal velocity of the contact line (Ren et al. (2010) \cite{Ren10}). In the numerical method, the governing equations for the fluid dynamics are coupled with an advection equation for a level-set function. The latter models the dynamics of the fluid interface. Following the standard practice, the interface conditions are taken into account by introducing a singular force on the interface in the momentum equation. This results in a single set of governing equations in the whole fluid domain. Similar to the treatment of the interface conditions, the contact angle condition is imposed by introducing a singular force, which acts in the normal direction of the contact line, into the Navier slip condition. The new boundary condition, which unifies the Navier slip condition and the contact angle condition, is imposed along the solid wall. The model is solved using the finite difference method. Numerical results, including a convergence study, are presented for the spreading of a droplet on both homogeneous and inhomogeneous solid walls, as well as the dynamics of a droplet on an inclined plate under gravity.

Review: American Freethinker: Elihu Palmer and the Struggle for Religious Freedom in the New Nation, by Kirsten Fischer

Review: <i>American Freethinker: Elihu Palmer and the Struggle for Religious Freedom in the New Nation</i>, by Kirsten Fischer

Fully implicit and accurate treatment of jump conditions for two-phase incompressible Navier–Stokes equations

We present a numerical method for two-phase incompressible Navier–Stokes equation with jump discontinuities in the normal projection of the stress tensor and in the material properties. Although the proposed method is only first-order accurate, it does capture discontinuities sharply, not neglecting nor omitting any component of the jump condition. Discontinuities in velocity gradient and pressure are expressed using a linear combination of singular force and tangential derivatives of velocities to handle jump conditions in a fully implicit manner. The linear system for the divergence of the stress tensor is constructed in the framework of the ghost fluid method, and the resulting saddle-point system is solved via an iterative procedure using recently introduced techniques by Egan and Gibou [9]. Numerical results support the inference that the proposed method converges in L∞ norms even when velocities and pressures are not smooth across the interface and can handle a large density ratio that is likely to appear in a real-world simulation.

The University and the Global Knowledge Society

The University and the Global Knowledge Society

"Papeles" comprados: procedimientos no ortodoxos implementados por guatemaltecos para adquirir documentos mexicanos de identificación personal

This article analyzes a series of extralegal procedures implemented by Guatemalans to acquire Mexican personal identification documents. The research focuses on the experiences of descendants of families who took refuge in Mexico during the 1980s and 1990s and returned to Guatemala between 1994 and 1996. These young people, born in Guatemala after their parents returned to their country of origin, employed the practice of buying Mexican birth certificates which were later used to enter Mexico legally. The fieldwork was carried out in two Guatemalan villages, as well as two Mexican ones, located in Cancun and Playa del Carmen. The main argument is that for them Mexican identification documents become a singular force that confers recognition and offers them the possibility to be incorporated into governmental logic which grants material benefits. Such forms of political imagination are related to the experiences of multiple documentation accumulated by older generations during their refuge period and are now encouraged by the Mexican State’s new border security strategy.