Scalar Theory Research Articles

Scaling theory for non-Hermitian topological transitions.

Understanding the critical properties is essential for determining the physical behavior of topological systems. In this context, scaling theories based on the curvature function in momentum space, the renormalization group (RG) method, and the universality of critical exponents have proven effective. In this work, we develop a scaling theory for non-Hermitian topological states of matter. We utilize the curvature function renormalization group (CRG) method, incorporating biorthonormal vectors for a 2 × 2 non-Hermitian Dirac model. This approach allows us to analyze the Wannier state correlation function (WCF) and determine the corresponding localization critical exponent. The CRG method successfully identifies topological phase transitions and locates stable and unstable fixed points. To account for non-Hermitian effects, we construct the curvature function in the generalized Brillouin zone using non-Bloch wave functions, enabling a comprehensive WCF and CRG analysis.

Theory of mind in trichotillomania: A cross-sectional comparison with healthy controls

Background Theory of mind (ToM) is the ability to make correct inferences from one’s own or another person’s mental states, such as thoughts, beliefs, desires, and intentions. Although there are a limited number of studies in the literature examining the social cognitive functions of patients with trichotillomania (TTM), no studies have evaluated ToM. This study aimed to compare the ToM skills of patients with TTM and healthy controls. Method The study included 40 patients who were diagnosed as having TTM according to DSM-5 criteria and 40 healthy controls matched for age, education, and sex. A Sociodemographic and Clinical Data Form, the Beck Depression Inventory (BDI), Beck Anxiety Inventory (BAI), Massachusetts General Hospital Hairpulling Scale (MGH-HPS), Toronto Alexithymia Scale (TAS-20), Reading the Mind in the Eyes Test (RMET), and the Dokuz-Eylül Theory of Mind Scale (DEToMS) were administered to the participants. Results Patients with TTM performed statistically significantly worse than healthy controls in terms of ToM, metaphor concept, empathic understanding, and faux pas scores. No statistically significant difference was found between the groups in terms of first-degree false belief, second-degree false belief, and irony concept scores. Depression, anxiety, and alexithymia scores of patients with TTM were statistically significantly higher than the control group. No significant correlation was found between ToM tests and anxiety, depression, alexithymia, disease severity, and disease duration in the TTM group. Conclusion Our findings show that there is an impairment in ToM skills in patients with TTM and that this impairment is independent of clinical features. Studies with larger samples are needed on this subject.

Exponential synchronization of bi-directional associative memory neural networks with delay on arbitrary time domains

Abstract We investigate the exponential synchronization of bi-directional associative memory neural networks with delays on a family of different time domains. By utilizing the theory of time scales, we provide stabilization results that are applicable to continuous-time, discrete-time, and general nonuniform hybrid time domains. Our approach employs a unified matrix-measure theory, a recent alternative to traditional Lyapunov functions, to establish exponential synchronization and design effective feedback laws. Notably, our methodology does not require symmetry or diagonality in the control gain matrix, distinguishing it from prior works. Furthermore, we explore various special cases of the considered systems and provide a detailed discussion highlighting the advantages of our findings over existing results. The effectiveness of our proposed criteria is demonstrated through small-scale and medium-scale simulated numerical examples across different time domains. Additionally, we apply our results to an example from the literature, showcasing the broad applicability and improved performance of our method in comparison to previous approaches.

Stress wave scaling theory of bar with variable cross-section

Stress wave scaling theory of bar with variable cross-section

Unravelling the electronic structure, bonding, and magnetic properties of inorganic dysprosocene analogues [Dy(E4)2]- (E = N, P, As, CH).

Organometallic sandwich complexes of Dy(III) ion are ubiquitous for designing high-temperature single-ion magnets with blocking temperatures close to the liquid nitrogen boiling point. Magnetic bistability at the molecular level makes them potential candidates for nano-scale information storage materials. In the present contribution, we have thoroughly investigated the electronic structure, bonding, covalency, and magnetic anisotropy of inorganic dysprosocene complexes with a general formula of [Dy(E4)2]- (where E = N, P, As, CH) using state-of-the-art scalar relativistic density functional theory (SR-DFT), and a multiconfigurational complete active space self-consistent field (CASSCF) method with the N-electron valence perturbation theory (NEVPT2). Geometry optimization calculations predict stabilization of the [Dy(E4)2]- complexes with a linear geometry and D4h local symmetry Dy(III) ion in [Dy(N4)2]- (1) and [Dy(P4)2]- (2) complexes, while a bent geometry has been observed for the [Dy(As4)2]- (3), [Dy(P2(CH)2)2]- (4), and [Dy(As2(CH)2)2]- (5) complexes. Energy decomposition analysis (EDA) and natural bonding orbital (NBO) calculations reveal sizable 5d-ligand covalency followed by 6s/6p and weak 4f-ligand covalency in complexes 1-5. Both the natural localized molecular orbitals (NLMOs) at the DFT level and ab initio-based ligand field theory (AILFT) at the NEVPT2 level of theory predict an increase in the Dy-ligand covalency as we move from N to As. Spin-Hamiltonian parameter analysis of complexes 1-5 reveals stabilization of the mJ |±15/2〉 as the ground state with highly axial g values (gxx ∼ gyy ∼ 0 and gzz ∼ 20) and the barrier height of 2902, 1214, 1104, 1845, and 1509 K for 1-5, respectively. The Orbach effective demagnetization barrier (Ueff) for complexes 1-5 ranges between 2416-1175 K, with a record Ueff value of 2416 K observed for 1. In addition, we have explored the role of heavy element effects on the magnetic anisotropy by turning off the spin-orbit coupling of the pnictogens (N, P, and As), and our calculations clearly predict that heavy atoms in the first coordination sphere help in increasing the barrier height for magnetic relaxation. Heavy elements like P and As significantly enhance the SOC contributions, thereby providing a platform for designing and optimizing Dy(III) complexes with tailored magnetic behaviors.

Linking Anxiolytic Action to Hippocampal "Theta"-A Personal History.

This paper provides a personal history of work starting with the discovery that anxiolytic drugs reduce hippocampal theta frequency. It includes parallel work on septal elicitation of theta carried out in Jeffrey Gray's laboratory in Oxford; a statement of my original scientific perspective on the work; and a description of later work in my laboratory in New Zealand confirming the function of theta rhythmicity per se and its mediation of the effects of anxiolytic drugs on behavior. I finish with comments on risk management with such experiments and their use in larger scale theory development.

Generalized Langevin equation for a tagged monomer in a Gaussian semiflexible polymer.

In this study, we present a comprehensive analysis of the motion of a tagged monomer within a Gaussian semiflexible polymer model. We carefully derived the generalized Langevin equation (GLE) that governs the motion of a tagged central monomer. This derivation involves integrating out all the other degrees of freedom within the polymer chain, thereby yielding an effective description of the viscoelastic motion of the tagged monomer. A critical component of our analysis is the memory kernel that appears in the GLE. By examining this kernel, we characterized the impact of bending rigidity on the non-Markovian diffusion dynamics of the tagged monomer. Furthermore, we calculated the mean-squared displacement of the tagged monomer using the derived GLE. Our theoretical findings were corroborated by the Langevin dynamics simulation and scaling theory. Our results not only show remarkable agreement with previously known results in certain limiting cases but also provide dynamic features over the entire timescale.

What are they all doing in that restaurant? Perspectives on the use of theory of mind

If “theory of mind” is conceived as reasoning in a strict sense, then it can be said to be useful only at certain times; however, this leaves the rest of social cognition hardly comprehensible. If “theory of mind” is used instead to refer to a mentalist ontology and the consequent awareness that we ourselves and the others function on mental states, then we need new approaches that explain the flow of social experience. To illustrate these points, we outline the general conceptual framework that underlies most empirical studies of theory of mind and discuss their pros and cons; then, we discuss the Theory of Mind Assessment Scale, a tool developed to investigate the complexity of theory of mind, which adopts a different perspective and has been successfully tested on numerous populations.

Fast simulation of the influence of a refractive free-form microstructure on a wave field based on scalar diffraction theory

We present a novel fast simulation approach to simulate the influence of refractive freeform microstructures on a wave field. The FRISP (Finite Refractive Index Selective Propagation) method combines the Rayleigh-Sommerfeld diffraction integral with a thin element approximation and provides a comprehensive framework for understanding the optical properties of these microstructures. The main advantage of this method is its reduced complexity, which leads to a remarkable reduction in computation time by more than two orders of magnitude compared to finite-difference time-domain (FDTD) methods. This efficiency facilitates the iterative optimization of refractive microstructures and thus represents a practical tool to improve this type of microstructures. The verification of the FRISP method is realized by comparing the focal position and spot size of refractive microstructures. For this purpose, we compare FDTD, Mie theory and experimental data on microspheres with the predictions of FRISP. This comparison demonstrates the robustness and reliability of the approach, emphasizes its validity and demonstrates it as a valuable tool for the design and analysis of microstructures.

Integral identities and universal relations for solitons

We show that any nonlinear field theory giving rise to static solutions with finite energy like, e.g., topological solitons, allows us to derive an infinite number of integral identities which any such solution has to obey. These integral identities can always be understood as being generated by field transformations and their related Noether currents. We also explain why all integral identities generated by coordinate transformations become trivial for Bogomolnyi-Prasad-Sommerfield (BPS) solitons, i.e., topological solitons which saturate a topological energy bound. Finally, we consider applications of these identities to a broad class of nonlinear scalar theories, including the Skyrme model. More concretely, we find nontrivial integral identities that can be seen as model-independent relations between certain physical properties of the solitons in such theories, and we comment on the possible connection between these new relations and those already found in the context of astrophysical compact objects. We also demonstrate the usefulness of said identities to estimate the precision of the numerical calculation of soliton observables. Published by the American Physical Society 2024

Fractional Inequalities for Exponentially s-Convex Functions on Time Scales

In this paper, we present new integral inequalities involving exponentially s-convex functions in the second sense on time scales. By utilizing the delta Riemann-Liouville fractional integral and the fractional Taylor formula, we establish upper bounds for functions that are n-times rd-continuously Δ-differentiable with exponentially s-convex properties. Our results provide novel insights into the theory of time scales, bridging the gap between discrete and continuous calculus. The application of fractional calculus on time scales is explored, and several well-known inequalities are employed to derive the main findings. These results have potential implications for further studies in fractional dynamic calculus and other related fields. AMS Subject Classification: 39A10, 39A11, 39A20.

Emergent polar order in nonpolar mixtures with nonreciprocal interactions

Phenomenological rules that govern the collective behavior of complex physical systems are powerful tools because they can make concrete predictions about their universality class based on generic considerations, such as symmetries, conservation laws, and dimensionality. While in most cases such considerations are manifestly ingrained in the constituents, novel phenomenology can emerge when composite units associated with emergent symmetries dominate the behavior of the system. We study a generic class of active matter systems with nonreciprocal interactions and demonstrate the existence of true long-range polar order in two dimensions and above, both at the linear level and by including all relevant nonlinearities in the Renormalization Group sense. We achieve this by uncovering a mapping of our scalar active mixture theory to the Toner-Tu theory of dry polar active matter by employing a suitably defined polar order parameter. We then demonstrate that the complete effective field theory-which includes all the soft modes and the relevant nonlinear terms-belongs to the (Burgers-) Kardar-Parisi-Zhang universality class. This classification allows us to prove the stability of the emergent polar long-range order in scalar nonreciprocal mixtures in two dimensions, and hence a conclusive violation of the Mermin-Wagner theorem.

Urban scaling theory: Answers to frequent questions

Since its start about 15 years ago, urban scaling research has become a vibrant component of the emerging field of urban science. Initially, this work focused on the identification of nonlinear relationships in urban quantities relative to population size, but more recently it has expanded to include efforts to explain observed scaling relationships in terms of new theory. We find that some misunderstandings have arisen in the literature concerning the nature and purpose of this work. Here, we address several persistent questions that have been raised with respect to urban scaling theory, clarify what we perceive to be its achievements and distinctiveness, and highlight questions and areas of opportunity for future work.

A Planck scale theory of time, with a fast early cosmological time rate, and rederivations for relativistic energy and time dilation

Among the issues to be resolved between general relativity and quantum mechanics are their differences about time. Block time has been weakened in two areas of its foundations recently: The small-scale reversibility has been falsified by experiments in quantum processes, and spacetime is now widely seen as emerging from unknown physics, rather than fundamental. This leaves room for differences to the nature of time. Here a theory of time is set out, in which light and matter arise in the small-scale structure of space, as waves in the dimensions themselves, traveling on the axes. It reinterprets special relativity, with two rederivations. The reasoning that led to block time, such as Penrose's version with three objects in one frame, is removed via a difference to frames that usually has no effect—the two observers are related to the event separately, as their relationships to it imply different, incompatible, positionings for the axes. This also leads to an explanation for light always moving at the same speed in relation to matter: With several objects moving differently, each is related to the light beam separately. In cosmology, new data suggest galaxies formed earlier than expected, with higher masses. And even earlier, inflation and variable speed of light theories both describe extremely rapid events. Planck scale time (PST) theory includes a specific mechanism for an overall time rate, which starts fast, then slows over time, and is consistent with supernova and gamma ray burst data. This allows galaxies more time to form, and in PST all matter's mass‐energy descends with the time rate (proportional time and energy changes in a gravitational field can be taken in the same way). This can also explain the “downsizing” sequence in galaxy formation, first described in 1996, in which stars in more massive galaxies formed earlier and quicker.

Quantization of Carrollian conformal scalar theories

In this work, we study the quantization of Carrollian conformal scalar theories, including two-dimensional (2D) magnetic scalar and three-dimensional (3D) electric and magnetic scalars. We discuss two different quantization schemes, depending on the choice of the vacuum. We show that the standard canonical quantization corresponding to the induced vacuum yields a unitary Hilbert space and the 2-point correlation functions in this scheme match exactly with the ones computed from the path integral. In the canonical quantization, the BMS symmetry can be realized without anomaly. On the other hand, for the quantization based on the highest-weight vacuum, it does not have a unitary Hilbert space. In 2D, the correlators in the highest-weight vacuum agree with the ones obtained by taking the c→0 limit of the 2D CFT, and there is an anomalous term in the commutation relations between the Virasoso generators, whose form is similar to the one in 2D CFT. In 3D, there is no good definition of the highest-weight vacuum without breaking the rotational symmetry. In our study, we find that the usual state-operator correspondence in CFT does not hold in the Carrollian case. Published by the American Physical Society 2024

From global imaginaries to local realities: marginalisation of multilingual identities in post-study abroad contexts

ABSTRACT There is growing recognition that study abroad is seen as a resource for shaping neoliberal subjects who possess the skills to join a mobile, globalised workforce. While existing research has explored the advantages study abroad offers sojourners in their careers, less attention has been accorded to how individuals experience return contexts in light of these social imaginaries of study abroad. This paper utilises theories of scale and positioning to examine the return experiences of 12 Japanese high-school students who spent a year abroad in various locations. Through qualitative analysis of interviews conducted a year after their return, our findings illustrate how the linguistic resources acquired by the informants abroad were marginalised within the local scale of the return classroom, particularly in languages other than English. Further, the results show how upon return, the informants struggled to occupy legitimate Japanese identities and were instead positioned as outsiders. We therefore argue that the tensions between globalising imaginaries of study abroad and local imaginaries of identity create a disjuncture, with ramifications for sojourners’ desire and ability to maintain multilingual repertoires cultivated abroad. This has implications for both individuals who elect to study abroad and for wider policy aims to develop globally competent workers.

Modeling the generation and control of Bessel-like beams generated by annular patterns on a digital micromirror device

Bessel beams have been generated using different methods, such as Axicon lens, digital micromirror device (DMD), etc. Due to the infinite energy requirement of ideal Bessel beams in all space, the generated Bessel beams are more appropriately called Bessel-like beams in practice, which are approximations of the ideal Bessel beams. In this work, we theoretically investigated the generation of Bessel-like beams using annular patterns loaded on a DMD based on the scalar diffraction theory. The model predictions were compared and verified with our previous experimental results. For the first time, the theoretical study shows that the DMD-generated Bessel-like beams have an additional amplitude term depending on the annular radius, ring thickness, and incident angle compared with ideal Bessel beams. Furthermore, we modeled the superposition of two Generated Bessel-like beams using two coaxial annular patterns on a DMD, which revealed the periodic intensity distribution along the z axis as predicted previously based on the superposition of two ideal coaxial Bessel beams. Both the simulations and experiments give a similar periodic length that is close to the theoretical values. The modeling results show that the DMD-based method could not only generate a reasonable approximation of the ideal Bessel beams with good controllability and engineering applications but more importantly, provide explicit formulas to guide the design of the annular patterns on the DMD in order to generate and control Bessel-like beams for practical applications.

Positivity bounds in scalar Effective Field Theories at one-loop level

Parameters in an effective field theory can be subject to certain positivity bounds if one requires a UV completion that obeys the fundamental principles of quantum field theory. These bounds are relatively straightforward at the tree level, but would become more obscure when loop effects are important. Using scalar theories as examples, we carefully exam the positivity bounds in a case where the leading contribution to a forward elastic amplitude arises at the one-loop level, and point out certain subtleties in terms of the implications of positivity bounds on the theory parameter space. In particular, the one-loop generated dimension-8 operator coefficients (that would be positive if generated at the tree level), as well as their β-functions are generally not subject to positivity bounds as they might correspond to interference terms of the cross sections under the optical theorem, which could have either sign. A strict positivity bound can only be implied when all contributions at the same loop order are considered, including the ones from dim-4 and dim-6 operator coefficients, which have important effects at the one-loop level. Our results may have important implications on the robustness of experimental tests of positivity bounds.

Boreal Winter Hadley Cell Contraction in Response to the Incorporation of a Comprehensive Ocean Surface Albedo in CESM2

AbstractThis study investigates the causes of shifts in the subsiding edge of the boreal winter Hadley cell (HC) in response to a comprehensive treatment of ocean surface albedo (OSA) in the fully coupled CESM2. The focus is on an in‐depth understanding of the atmospheric dynamical processes that influence the HC subsiding edge. Two sets of experiments were performed: one utilizing the default OSA, and the other employing the comprehensive OSA that accounts for realistic physical mechanisms. The results show that implementing the comprehensive OSA simulates an El Niño‐like warming pattern in reference to the default experiment, which leads to an HC contraction. Examination of zonal mean momentum dynamics in the upper troposphere reveals that variations in meridional winds, crucial for determining the HC extent, are primarily driven by the differences in the horizontal eddy momentum flux derivative. The findings indicate that the equatorward shift in meridional temperature gradients enhances subtropical zonal winds and baroclinicity along their equatorial flanks, amplifying equatorward‐propagating Rossby waves. This, in turn, alters the eddy momentum flux, reshaping the pattern of the derivatives of horizontal eddy momentum flux, constraining meridional winds, and resulting in the equatorward movement of the HC subsiding edge. A scaling theory further supports the results of the HC contraction, showing that the increased subtropical zonal winds and the equatorward shift of the Intertropical Convergence Zone (ITCZ) elevate the atmospheric angular momentum and eventually limit the expansion of the HC.

"Our Cry as Women Leaders": Crisis Response Intervention, Customary Governance, and the Masculinization of Peace in Solomon Islands

This discussion examines how and why the peacebuilding environment in Solomon Islands presents profound constraints for women despite the promises of global, regional, and national policy stipulating the importance of this activity. The analysis draws on theories of scale to explain how gendered geometries of power are configured in the Solomon Islands peacebuilding environment. These power geometries are shaped by interplaying local and global factors and have limited the space that is open to women peacebuilders. A "crisis response" orientation to Australian-led conflict stabilization missions has been coupled with a national bureaucratic tendency to equate "customary governance" with peacebuilding. Both trends have augmented masculine power and constrained the space for women to engage in conflict mediation. As I show, these developments contradict United Nations Women Peace and Security principles, set out in United Nations Security Council Resolution 1325 and localized in National Action Plans developed in Australia and in Solomon Islands. These expressly stipulate the importance of supporting women's contributions to peacebuilding when conflict flares. The article's analysis makes clear how women continue to push against these constraints, but against overwhelming pressures. It concludes with the claim that conflict mediation processes can only be made more durable in Solomon Islands if the discriminatory gendered geometries of power identified are confronted and greater emphasis is placed on women's customary authority and capacities as peacebuilders.