Analytical Arguments Research Articles

A study of nonlocal spatially heterogeneous logistic equation with harvesting

We study a class of nonlocal reaction–diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic operators, sum of fractional Laplacians of different order etc. We study the existence, uniqueness and multiplicity results of the solutions to the steady state equation. We also consider the parabolic counterpart and establish the long time asymptotic of the solutions. Our proof techniques rely on both analytic and probabilistic arguments.

Aspects of pseudoentropy in field theories

In this article, we explore properties of pseudo entropy [1] in quantum field theories and spin systems from several approaches. Pseudo entropy is a generalization of entanglement entropy such that it depends on both an initial and final state and has a clear gravity dual via the AdS/CFT. We numerically analyze a class of free scalar field theories and the XY spin model. This reveals the basic properties of pseudo entropy in many-body systems, namely, the area law behavior, the saturation behavior, and the non-positivity of difference between the pseudo entropy and averaged entanglement entropy in the same quantum phase. In addition, our numerical analysis finds an example where the strong subadditivity of pseudo entropy gets violated. Interestingly we find that the non-positivity of the difference can be violated only if the initial and final states belong to different quantum phases. We also present analytical arguments which support these properties by both conformal field theoretic and holographic calculations. When the initial and final states belong to different topological phases, we expect a gapless mode localized along an interface, which enhances the pseudo entropy leading to the violation of the non-positivity of the difference. Moreover, we also compute the time evolution of pseudo entropy after a global quench, were we observe that the imaginary part of pseudo entropy shows interesting characteristc behavior.

Windowed backoff algorithms for WiFi: theory and performance under batched arrivals

Binary exponential backoff (BEB) is a decades -old algorithm for coordinating access to a shared channel. In modern networks, BEB plays a crucial role in WiFi and other wireless communication standards. Despite this track record, well-known theoretical results indicate that under bursty traffic, BEB yields poor makespan, and superior algorithms are possible. To date, the degree to which these findings impact performance in wireless networks has not been examined. Here, we investigate a challenging case for BEB: a single burst (batch) of packets that simultaneously contend for access to a wireless channel. Using Network Simulator 3, we incorporate into IEEE 802.11g several newer algorithms that have theoretically-superior makespan guarantees. Surprisingly, we discover that these newer algorithms underperform BEB. Investigating further, we identify as the culprit a common abstraction regarding the cost of collisions. Our experimental results are complemented by analytical arguments that the number of collisions—and not solely makespan—is an important metric to optimize. We propose a new theoretical model that accounts for the cost of collisions, and derive new asymptotic bounds on the makespan for BEB and the newer backoff algorithms that align with our experimental findings. Finally, we argue that these findings have implications for the design of backoff algorithms in wireless networks.

A graphic turn for Canadian foreign policy: insights from systemism

ABSTRACT The application of systemism, an innovative and user-friendly technique for generating lucid, graphic summaries of analytical arguments, can enhance the study of Canadian foreign policy. As research and pedagogy on Canada and international relations move forward, its content becomes increasingly vast and intellectually diverse. Systemism offers both a means and a method toward enhanced communication in the face of challenges posed by the rapid expansion of topics and the proliferation of new theories and terminology in the fast-paced world of the new millennium. This is the motivation for a special issue of CFPJ that will show systemism in action across a wide range of issues and locations. This introductory article will proceed in four sections. The first section provides an overview of the project as a whole. Section two introduces systemism as a graphic approach toward the communication of ideas. The third section applies systemism to convey the framework for analysis from the standard textbook in the field – The Politics of Canadian Foreign Policy (Nossal, K. R., Roussel, S., & Paquin, S. The politics of Canadian Foreign Policy. Queen’s policy studies series (4th ed.). Montreal: McGill-Queen’s University Press, 2015). Section four outlines the articles that follow in making up the special issue.

Evolution of globular-cluster systems of ultra-diffuse galaxies due to dynamical friction in MOND gravity

Context. Dynamical friction can be used to distinguish Newtonian gravity and modified Newtonian dynamics (MOND) because it works differently in these frameworks. This concept, however, has yet to be explored very much with MOND. Previous simulations showed weaker dynamical friction during major mergers for MOND than for Newtonian gravity with dark matter. Analytic arguments suggest the opposite for minor mergers. In this work, we verify the analytic predictions for MOND by high-resolution N-body simulations of globular clusters (GCs) moving in isolated ultra-diffuse galaxies (UDGs). Aims. We test the MOND analog of the Chandrasekhar formula for the dynamical friction proposed by Sánchez-Salcedo on a single GC. We also explore whether MOND allows GC systems of isolated UDGs to survive without sinking into nuclear star clusters. Methods. The simulations are run using the adaptive-mesh-refinement code Phantom of Ramses. The mass resolution is 20 M⊙ and the spatial resolution 50 pc. The GCs are modeled as point masses. Results. Simulations including a single GC reveal that, as long as the apocenter of the GC is over about 0.5 effective radii, the Sánchez-Salcedo formula works excellently, with an effective Coulomb logarithm increasing with orbital circularity. Once the GC reaches the central kiloparsec, its sinking virtually stops, likely because of the core stalling mechanism. In simulations with multiple GCs, many of them sink toward the center, but the core stalling effect seems to prevent them from forming a nuclear star cluster. The GC system ends up with a lower velocity dispersion than the stars of the galaxy. By scaling the simulations, we extend these results to most UDG parameters, as long as these UDGs are not external-field dominated. We verify analytically that approximating the GCs by point masses has little effect if the GCs have the usual properties, but for massive GCs such as those observed in the NGC 1052-DF2 galaxy, further simulations with resolved GCs are desirable.

Low-temperature universal dynamics of the bidimensional Potts model in the large q limit

We study the low temperature quench dynamics of the two-dimensional Potts model in the limit of a large number of states, q ≫ 1. We identify a q-independent crossover temperature (the pseudo spinodal) below which no high-temperature metastability stops the curvature driven coarsening process. At short length scales, the latter is decorated by freezing for some lattice geometries, notably the square one. With simple analytic arguments, we evaluate the relevant time-scale in the coarsening regime, which turns out to be of Arrhenius form and independent of q for large q. Once taken into account, dynamic scaling is universal.

Z2 lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation

Kitaev's toric code is an exactly solvable model with $\mathbb{Z}_2$-topological order, which has potential applications in quantum computation and error correction. However, a direct experimental realization remains an open challenge. Here, we propose a building block for $\mathbb{Z}_2$ lattice gauge theories coupled to dynamical matter and demonstrate how it allows for an implementation of the toric-code ground state and its topological excitations. This is achieved by introducing separate matter excitations on individual plaquettes, whose motion induce the required plaquette terms. The proposed building block is realized in the second-order coupling regime and is well suited for implementations with superconducting qubits. Furthermore, we propose a pathway to prepare topologically non-trivial initial states during which a large gap on the order of the underlying coupling strength is present. This is verified by both analytical arguments and numerical studies. Moreover, we outline experimental signatures of the ground-state wavefunction and introduce a minimal braiding protocol. Detecting a $\pi$-phase shift between Ramsey fringes in this protocol reveals the anyonic excitations of the toric-code Hamiltonian in a system with only three triangular plaquettes. Our work paves the way for realizing non-Abelian anyons in analog quantum simulators.

Modersmålsämnets legitimitet i ett förändrat politiskt landskap - En analys av svensk riksdagsdebatt under 2010-talet

The legitimacy of the mother tongue subject in a changing political landscape: An analysis of Swedish parliamentary debate in the twenty-tens. This paper highlights and discusses the arguments in favor of, or against Mother Tongue Instruction (MTI) in Swedish parliamentary debate between 2010 and 2020. New to this decade is the entrance of yet another nationalist and populist party with the abolishment of MTI on its political agenda. Building on a critical discourse analytical frame and argumentation analysis, we discuss this party’s rhetoric on MTI – based in an Othering discourse and the construction of MTI as a path to alienation – and the parliamentary counter-voices. The latter mainly concern the role of MTI for development of Swedish and learning in other school subjects, implying that MTI in its own right is subordinated. We argue that this counter-discourse represents a shift in how MTI is legitimized – and in fact plays into assimilationists’ hands – compared to the pluralistic ideology that initially made way for MTI. The importance of scrutinizing political rhetoric is stressed to anticipate political action.

Excess wings and asymmetric relaxation spectra in a facilitated trap model.

In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally activated dynamics of glassy systems. We fully characterize the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the strength of dynamic facilitation, combining numerical results and analytic arguments. Dynamic facilitation generically accelerates the relaxation of the deepest traps, thus making relaxation spectra strongly asymmetric, with an apparent "excess" signal at high frequencies. For well-chosen values of the parameters, the obtained spectra mimic experimental results for organic liquids displaying an excess wing. Overall, our results identify the minimal physical ingredients needed to describe excess processes in the relaxation spectra of supercooled liquids.

Wigner Crystallization of Electrons in a One-Dimensional Lattice: A Condensation in the Space of States.

We study the ground state of a system of spinless electrons interacting through a screened Coulomb potential in a lattice ring. By using analytical arguments, we show that, when the effective interaction compares with the kinetic energy, the system forms a Wigner crystal undergoing a first-order quantum phase transition. This transition is a condensation in the space of the states and belongs to the class of quantum phase transitions discussed in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021).JPAMB51751-811310.1088/1751-8121/aba144]. The transition takes place at a critical value r_{s}_{c} of the usual dimensionless parameter r_{s} (radius of the volume available to each electron divided by effective Bohr radius) for which we are able to provide rigorous lower and upper bounds. For large screening length these bounds can be expressed in a closed analytical form. Demanding MonteCarlo simulations allow to estimate r_{s}_{c}≃2.3±0.2 at lattice filling 3/10 and screening length 10 lattice constants. This value is well within the rigorous bounds 0.7≤r_{s}_{c}≤4.3. Finally, we show that if screening is removed after the thermodynamic limit has been taken, r_{s}_{c} tends to zero. In contrast, in a bare unscreened Coulomb potential, Wigner crystallization always takes place as a smooth crossover, not as a quantum phase transition.

On the interaction between fast tides and convection

ABSTRACT The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new idea was however recently proposed by Terquem (2021), who suggested Reynolds stresses involving correlations between tidal flow components dominate the interaction instead of correlations between convective flow components as usually assumed. They further showed that this can potentially significantly enhance tidal dissipation for fast tides in many applications. Motivated by the importance of this problem for tidal dissipation in stars and planets, we directly compute this new term using analytical arguments and global spherical simulations using Boussinesq and anelastic hydrodynamic models. We demonstrate that the new term proposed by Terquem vanishes identically for equilibrium tides interacting with convection in both Boussinesq and anelastic models; it is therefore unlikely to contribute to tidal dissipation in stars and planets.

Spontaneous dimensional reduction and ground state degeneracy in a simple chain model.

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first-order transition from a high-temperature random coil phase to a highly unusual low-temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures [we call these PoSSuM (Planar Structures with Secondary Motifs)] in the phase and protein native state structures.

Optimal test-kit-based intervention strategy of epidemic spreading in heterogeneous complex networks.

We propose a deterministic compartmental model of infectious disease that considers the test kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with an analytical argument) is provided to reveal the effective reduction of the final outbreak size and the peak of infection as a function of basic reproduction number in a single patch. Furthermore, to study the impact of long and short-distance human migration among the patches, we consider heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We numerically confirm that implementation of test kits in a fraction of nodes (patches) having larger degrees or betweenness centralities can reduce the peak of infection (as well as the final outbreak size) significantly. A next-generation matrix-based analytical treatment is provided to find out the critical transmission probability in the entire network for the onset of epidemics. Finally, the optimal intervention strategy is validated in two real networks: the global airport network and the transportation network of Kolkata, India.

Stoner , Kathryn E. Russia Resurrected: Its Power and Purpose in a New Global Order (review)

REVIEWS 593 (p. 110), ‘neoliberal proselytism’ (p. 111) and ‘constitutional expertise at the expense of popular participation’ (p. 113) reads at times like an ahistorical mirror-image of the anti-liberal conspiracy theories about the transition from Communism currently pedalled by conservative populists in Hungary, Poland and elsewhere. It leaves little scope for recognizing the agency of ordinary Eastern Europeans, whether before, during, or after 1989, and their capacity to contest, subvert or reinterpret hegemonic discourses within the context of their own daily lives and experiences. Indeed, for all the lip-service the authors pay to the possibility of alternative trajectories or contrary political imaginaries in their concluding remarks, for much of the book they are in danger of simply replacing one teleological reading of 1989 with another. Department of Humanities Matthew Stibbe Sheffield Hallam University Stoner, Kathryn E. Russia Resurrected: Its Power and Purpose in a New Global Order. Oxford University Press, Oxford and New York, 2020. xix + 317 pp. Figures. Tables. Notes. Index. £22.99. In Russia Resurrected Kathryn Stoner offers a comprehensive and through overview of Russian foreign policy, a substantial contribution to the important debate over Russia’s foreign policy goals. Vladimir Putin has marshalled Russia’s modest economic resources to stabilize the economy, rebuild the military and project power abroad. Russia makes up for its modest power resources with willingness to take risks and be a ‘disrupter’ of international norms (p. 4). Stoner argues that Russia’s confrontational posture is not ‘natural destiny’ but a ‘strategic choice’ (p. 5) which does not reflect Russia’s national interests. Rather, it is ‘a reaction to domestic political exigencies and an attempt to meet the need to maintain popular support for an increasingly unpopular autocratic regime’ (p. 20). The good news is that Putin’s regime is ‘inherently fragile’ (p. 247), because of the lack of democratic accountability and the uncertainty of succession. Stoner disagrees with Realists who explain Russia’s security posture by referencing deep geographical and historical conditions (p. 238), arguing that ‘[t]he use of Russian power resources abroad is not predetermined by great power politics, geography, or history’ (p. 262). Geography and history are not sufficient to explain why Russia suddenly became more aggressive after 2008. Stoner also argues that ‘Russian capabilities have been underestimated because the wrong measures of power tend to be employed’ (p. 275). She seeks ‘to present a multidimensional understanding of Russian power resources SEER, 99, 3, JULY 2021 594 beyond the traditional means of men, military, and money’. But most of her account relies on quite traditional measures of power, such as the size of Russia’s GDP, population, military spending and numbers of weapons. There are few references to Russian-language sources. The main analytical arguments are laid out in chapters one and eight. Chapters two to seven offer detailed and encyclopaedic descriptions of various dimensions of Russian power. The book therefore is useful as a reference work, but not so easy to read through at one sitting. It would have been nice to see the arguments from chapters one and eight used to structure the analysis in the intervening chapters. Chapter two summarizes Russia’s relations with the post-Soviet states, country by country, while chapter three addresses the ‘far abroad’ — China only gets three pages (p. 109–12): the same as sub-Saharan Africa (pp. 103–06). Chapter four examines the economy, chapter five society, chapter six hard power and chapter seven soft power. Chapters four and five rely on data from sources such as the World Bank and OECD, comparing Russia with other leading powers. No sources are given for the charts in chapter four, though the sources are identified for the charts in chapter five. It is more convenient to look up the data on the internet, where the charts are easier to read and there are precise numbers for each year. Stoner is upbeat about the economy but downbeat about social trends. She describes Russia’s economic performance since 1991 as ‘impressive’ (p. 122). She denies that Russia is a ‘classically oil-cursed state’ (p. 134), saying it ‘was at least modestly successful in diversifying its export structure’ (p. 144). While it is...

(In)Segurança no campo da extensão universitária:micropolíticas das afetações com crianças na periferia / (In)Security in the field of university extension:micropolitics of affectations with children in the periphery

This text aims to guide an analytical debate from the affections experienced by a researcher teacher when accessing a peripheral territory in the city of Fortaleza-CE, as well as presenting the reasons that led her to undertake the crossing to the other side of this divided city and the repercussions of this on the actions of an Extension project. The relevance of this writing is to promote a critical reflection on the binomial security / insecurity that crosses us in the context of university extension. What is the reality limit of (in)security? What paralyzing and mobilizing affects can we access in this academic activity’s territories? In order to dialogue with these questions, we chose to cut scenes of this insertion in the periphery, presenting some micropolitics resulting from the affectations produced by the participation of the subjects involved in this project, through analyzes of the relationship between the participating children and the academic team; the relationship of these children with their neighborhood and the city (beyond the “walls” of the periphery).

Carnap und die Farben

In the analytical colour debate there are currently two positions facing each other: color objectivism and color subjectivism. For color objectivists, colors are purely physical properties, whereas for color subjectivists they are phenomenal properties that are ontologically dependent on subjects. Although both positions have strong arguments, a stalemate and idleness in the debate has been evident for decades that requires explanation. In this essay I will show, on the basis of some considerations of Carnap's color view, what causes the stalemate and idleness situation structurally and how it is 'solved' after Carnap.

Intensity correlation OCT is a classical mimic of quantum OCT providing up to twofold resolution improvement

Quantum Optical Coherence Tomography (Q-OCT) uses quantum properties of light to provide several advantages over its classical counterpart, OCT: it achieves a twice better axial resolution with the same spectral bandwidth and it is immune to even orders of dispersion. Since these features are very sought-after in OCT imaging, many hardware and software techniques have been created to mimic the quantum behaviour of light and achieve these features using traditional OCT systems. The most recent, purely algorithmic scheme—an improved version of Intensity Correlation Spectral Domain OCT named ICA-SD-OCT—showed even-order dispersion cancellation and reduction of artefacts. The true capabilities of this method were unfortunately severely undermined, both in terms of its relation to Q-OCT and its main performance parameters. In this work, we provide experimental demonstrations as well as numerical and analytical arguments to show that ICA-SD-OCT is a true classical equivalent of Q-OCT, more specifically its Fourier domain version, and therefore it enables a true two-fold axial resolution improvement. We believe that clarification of all the misconceptions about this very promising algorithm will highlight the great value of this method for OCT and consequently lead to its practical applications for resolution- and quality-enhanced OCT imaging.

Mesh sensitivity in numerical models of strain-weakening systems

This paper advances a framework for evaluating mesh sensitivity in numerical models of systems involving strain-weakening materials, and demonstrates its application in the case study of the failure at the Mount Polley TSF in Canada. Numerical studies are combined with analytical arguments and physical evidence to establish that this failure was caused in part by the localisation of strain in a shear band with a thickness 0 < hsb ≤ 12.5 cm, and to rule out the possibility of slippage along a pre-sheared plane in the foundation. The range of model responses is bound by an upper limit representing the least conservative case of “no weakening,” and a lower limit representing the most conservative case of strain localisation within an infinitely thin shear band, predicting the highest and the lowest stability levels, respectively. The limit states are discoverable using a new method presented here. The model’s convergence is shown to vary at mesh discretisation levels above the minimum established by the upper limit state analysis; higher mesh resolutions yield lower stability levels, approaching asymptotically the floor value established by the lower limit state analysis. A conceptual relationship between a model’s discretisation, the shape of the strain-weakening curve and convergence is formulated.

Radiation reaction from soft theorems

Radiation reaction (RR) terms at the third post-Minkowskian (3PM) order have recently been found to be instrumental in restoring smooth continuity between the non-relativistic, relativistic, and ultra-relativistic (including the massless) regimes. Here we propose a new and intriguing connection between RR and soft (bremsstrahlung) theorems which short-circuits the more involved conventional loop computations. Although first noticed in the context of the maximally supersymmetric theory, unitarity and analyticity arguments support the general validity of this 3PM-order connection that we apply, in particular, to Einstein's gravity and to its Jordan-Brans-Dicke extension. In the former case we find full agreement with a recent result by Damour obtained through a very different reasoning.

Interaction-resistant metals in multicomponent Fermi systems

We analyze two different fermionic systems that defy Mott localization showing a metallic ground state at integer filling and very large Coulomb repulsion. The first is a multiorbital Hubbard model with a Hund's coupling (this physics has been widely studied, and the new metallic state is called a Hund's metal), and the second is a SU(3) Hubbard model with a patterned single-particle potential designed to display a similar interaction-resistant metal in a setup which can be implemented with $\mathrm{SU}(N)$ ultracold atoms. With simple analytical arguments and exact numerical diagonalization of the Hamiltonians for a minimal three-site system, we demonstrate that the interaction-resistant metal emerges in both cases as a compromise between two different insulating solutions which are stabilized by different terms of the models. This provides strong evidence that the Hund's metal is a specific realization of a more general phenomenon which can be realized in various strongly correlated systems.