Dynamical Field Theory Research Articles

Efficient Modeling of High-Generation Dendrimers in Solution Using Dynamical Self-Consistent Field Theory

Efficient Modeling of High-Generation Dendrimers in Solution Using Dynamical Self-Consistent Field Theory

Smooth generalized symmetries of quantum field theories

Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of ∞-categories. According to a geometric version of the cobordism hypothesis, such QFTs collectively assemble themselves into objects in an ∞-topos of smooth spaces. We show how this allows one to define and study generalized global symmetries of such QFTs. The symmetries are themselves smooth, so the ‘higher-form’ symmetry groups can be endowed with, e.g., a Lie group structure.Among the more surprising general implications for physics are, firstly, that QFTs in spacetime dimension d, considered collectively, can have d-form symmetries, going beyond the known (d−1)-form symmetries of individual QFTs and, secondly, that a global symmetry of a QFT can be anomalous even before we try to gauge it, due to a failure to respect either smoothness (in that a symmetry of an individual QFT does not smoothly extend to QFTs collectively) or locality (in that a symmetry of an unextended QFT does not extend to an extended one).Smoothness anomalies are shown to occur even in 2-state systems in quantum mechanics (here formulated axiomatically by equipping d=1 spacetimes with a metric, an orientation, and perhaps some unitarity structure). Locality anomalies are shown to occur even for invertible QFTs defined on d=1 spacetimes equipped with an orientation and a smooth map to a target manifold. These correspond in physics to topological actions for a particle moving on the target and the relation to an earlier classification of such actions using invariant differential cohomology is elucidated.

Investigating microstructure evolution in block copolymer membranes.

Block copolymer self-assembly in conjunction with nonsolvent-induced phase separation (SNIPS) has been increasingly leveraged to fabricate integral-asymmetric membranes. The large number of formulation and processing parameters associated with SNIPS, however, has prevented the reliable construction of high performance membranes. In this study, we apply dynamical self-consistent field theory to model the SNIPS process and investigate the effect of various parameters on the membrane morphology: solvent selectivity, nonsolvent selectivity, initial film composition, and glass transition composition. We examine how solvent selectivity and concentration of polymers in the film impact the structure of micelles that connect to form the membrane matrix. In particular, we find that preserving the order in the surface layer and forming a connection between the supporting and surface layer are nontrivial and sensitive to each parameter studied. The effect of each parameter is discussed, and suggestions are made for successfully fabricating viable block copolymer membranes.

Ideonamic: An integrative computational dynamic model of ideomotor learning and effect-based action control.

According to ideomotor theory, actions are represented, controlled, and retrieved in terms of the perceptual effects that these actions experientially engender. When agents perform a motor action, they observe its subsequent perceptual effects and establish action-effect associations. When they want to achieve this effect at a later time, they use the action-effect associations to preactivate the action by internally activating the effect representation. Ideomotor theory has received extensive support in recent years. To capture this particular effect-based view on action control and goal-directed behavior, we developed IDEONAMIC, an integrative computational model based on dynamic field theory that represents the specific components of the action control process as dynamic neural fields. We show that IDEONAMIC applies conveniently to different types of experimental ideomotor settings, simulates key findings, generates novel predictions from the dynamics of data, and allows reapproaching the underlying cognitive mechanisms from a computational point of view. We encourage the application of IDEONAMIC to more types of ideomotor settings to gain insights into effect-based action control. The model is available at https://osf.io/hbc6n. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Designing the color of electric motorcycle products emotionally based on the dynamic field theory and deep learning

Current research in Product Color Emotional Design (PCED) often encounters limitations due to the ambiguity in users' emotional information expression, potentially compromising the effectiveness of the design scheme. This paper presents a novel PCED methodology that integrates dynamic field theory with deep learning, thus enabling one-stop generation from user feature labels to product color. Consequently, a product color design system is established, capable of generating color design schemes that align with users' emotional needs by solely incorporating user feature labels. This approach mitigates potential inaccuracies in generation results that could stem from users' direct expression of emotional information. The validity and applicability of the proposed method are demonstrated through a case study focusing on the color emotion design of an electric motorcycle.

Self-consistent dynamical field theory of kernel evolution in wide neural networks *

We analyze feature learning in infinite-width neural networks trained with gradient flow through a self-consistent dynamical field theory. We construct a collection of deterministic dynamical order parameters which are inner-product kernels for hidden unit activations and gradients in each layer at pairs of time points, providing a reduced description of network activity through training. These kernel order parameters collectively define the hidden layer activation distribution, the evolution of the neural tangent kernel (NTK), and consequently, output predictions. We show that the field theory derivation recovers the recursive stochastic process of infinite-width feature learning networks obtained by Yang and Hu with tensor programs. For deep linear networks, these kernels satisfy a set of algebraic matrix equations. For nonlinear networks, we provide an alternating sampling procedure to self-consistently solve for the kernel order parameters. We provide comparisons of the self-consistent solution to various approximation schemes including the static NTK approximation, gradient independence assumption, and leading order perturbation theory, showing that each of these approximations can break down in regimes where general self-consistent solutions still provide an accurate description. Lastly, we provide experiments in more realistic settings which demonstrate that the loss and kernel dynamics of convolutional neural networks at fixed feature learning strength are preserved across different widths on a image classification task.

Neural dynamic foundations of a theory of higher cognition: the case of grounding nested phrases.

Because cognitive competences emerge in evolution and development from the sensory-motor domain, we seek a neural process account for higher cognition in which all representations are necessarily grounded in perception and action. The challenge is to understand how hallmarks of higher cognition, productivity, systematicity, and compositionality, may emerge from such a bottom-up approach. To address this challenge, we present key ideas from Dynamic Field Theory which postulates that neural populations are organized by recurrent connectivity to create stable localist representations. Dynamic instabilities enable the autonomous generation of sequences of mental states. The capacity to apply neural circuitry across broad sets of inputs that emulates the function call postulated in symbolic computation emerges through coordinate transforms implemented in neural gain fields. We show how binding localist neural representations through a shared index dimension enables conceptual structure, in which the interdependence among components of a representation is flexibly expressed. We demonstrate these principles in a neural dynamic architecture that represents and perceptually grounds nested relational and action phrases. Sequences of neural processing steps are generated autonomously to attentionally select the referenced objects and events in a manner that is sensitive to their interdependencies. This solves the problem of 2 and the massive binding problem in expressions such as "the small tree that is to the left of the lake which is to the left of the large tree". We extend earlier work by incorporating new types of grammatical constructions and a larger vocabulary. We discuss the DFT framework relative to other neural process accounts of higher cognition and assess the scope and challenges of such neural theories.

A dynamic neural field model of leaky prosody: proof of concept

Recent work has shown that lexical items come to take on the phonetic characteristics of the prosodic environments in which they are typically produced, a phenomenon referred to as "leaky prosody". Focusing on pitch patterns in Mandarin, we show that leaky prosody can be derived from a flat (i.e., non-transformational, non-optimizing) model of speech production. Formalized using Dynamic Field Theory, in our model, lexical, phonological, and prosodic inputs each exert forces on a Dynamic Neural Field representing pitch. Notably, the forces exerted by these inputs reflect surface distributions in a large corpus of spontaneous speech. Our simulations showed that the flat model derives the short timescale effect of prosodic prominence on pitch production as well as the longer timescale effect of leaky prosody. By updating lexical items based on surface phonetic form, words that are consistently produced in high/low prosodic prominence positions take on the phonetic characteristics of those environments.

The Process-Directed Self-Assembly of Block Copolymer Particles.

The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, χAB ) and the selectivity of solvent toward one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, it is identified that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. The findings lead to an effective way of tailoring nanostructure of BCP particles for various industrialapplications.

Dynamical Gauge Fields with Bosonic Codes.

The quantum simulation of dynamical gauge field theories offers the opportunity to study complex high-energy physics with controllable low-energy devices. For quantum computation, bosonic codes promise robust error correction that exploits multiparticle redundancy in bosons. Here, we demonstrate how bosonic codes can be used to simulate dynamical gauge fields. We encode both matter and dynamical gauge fields in a network of resonators that are coupled via three-wave mixing. The mapping to a Z_{2} dynamical lattice gauge theory is established when the gauge resonators operate as Schrödinger cat states. We explore the optimal conditions under which the system preserves the required gauge symmetries. Our findings promote realizing high-energy models using bosonic codes.

Inversion of one‐dimensional parameters of horizontal multi‐layer soil model based on dynamic state electromagnetic field theory and ant colony optimization algorithm

AbstractBuilding a reliable soil model is a prerequisite for accurately calculating the ground potential distribution of the grounding grid. Research shows that the soil electrical parameters are frequency‐dependent, so frequency domain inversion of soil parameters should consider the soil inhomogeneity and the frequency characteristic of parameters. A method for retrieving parameters of horizontal multilayer soil model is proposed. The theoretical formula of apparent complex resistivity with considering dynamic state electromagnetic field theory is derived from Green's function. Discrete dynamic state complex image method is introduced to solve the infinite integral in Green's function. Ant colony optimization algorithm is applied to optimize the inversion process of soil parameters. In the first stage, applicability of this method is confirmed by interpreting field data under DC field. DC parameters including DC resistivity, thickness and number of layer are determined. The performance of different optimization algorithms in terms of computational efficiency is compared at this stage. In the second stage, soil resistivity and relative dielectric constant are retrieved by inverting frequency domain experimental data. Different representations based on quasi‐static electromagnetic field and dynamic state electromagnetic field theories are taken into account. The frequency characteristic of soil parameters is concluded by discussing the inversion results. In the study of parameter inversion of horizontal multi‐layer soil model, our method has shown strong performance in computational efficiency and accuracy of inversion results.

О некоторых строгих результатах в теории конденсированного состояния

The work contains a critical analysis of the methods and results currently used and applied in the theory of condensed matter. A unified mathematical apparatus has been developed - the method of functional integration which is equally applicable to all main distributions of statistical physics: microcanonical, canonical, and grand canonical ensembles. Within the framework of this method, an exact factorization of the configuration integral with respect to atomic coordinates was performed and a connection between the microcanonical and canonical ensembles was established. It is shown that interatomic interactions can be eliminated by renormalizing external random fields, and random external fields can be eliminated by renormalizing interatomic potentials. A new formulation of problems of equilibrium statistical mechanics as a dynamic field theory with a Hamiltonian depending on temperature is proposed.

The Anion-Dominated Dynamic Coordination Field in the Electrolytes for High-Performance Lithium Metal Batteries

Electrolyte plays a dominant role in solving the various challenges of Li-metal batteries (LMBs). The complex competition coordination and diversity of the anion coordination clusters in electrolytes are still unclear. In this paper, an anion-dominated dynamic coordination field (ADCF) theory is proposed to reasonably explain the coordination behavior in the high-concentration, localized high-concentration, and weak-ionization localized high-concentration electrolytes, which is based on specific characterizations and theoretical calculations. The novel model selects the anions as the center of the whole molecular groups/clusters, while the Li+ acts as the counterion or carrier, which can promote the dynamic and elastic movement of the whole cluster. The specific coordination clusters could remarkably enhance the interaction between TFSI− and Li+, and make the counterion composition of Li+ increase. The confinement effect of the coordination field provides a difficult ionization atmosphere for the Li+, and enables clusters to preferentially adsorb on the Li surface, and construct a specific solid electrolyte interphase (SEI). Furthermore, the electrode/electrolyte interface kinetics and the growth of lithium dendrites are systematically investigated. These new viewpoints of coordination behavior provide inclusive strategies in the electrolyte design, and promote further research of the charge transfer or solution behavior.

Modeling Microstructure Formation in Block Copolymer Membranes Using Dynamical Self-Consistent Field Theory.

Block copolymers have attracted recent interest as candidate materials for ultrafiltration membranes, due to their ability to form isoporous integral-asymmetric membranes by the combined processes of self-assembly and nonsolvent-induced phase separation (SNIPS). However, the dependence of surface layer and substructure morphologies on the processing variables associated with SNIPS is not well understood nor is the interplay between microphase and macrophase separation in block copolymers undergoing such coagulation. Here, we use dynamical self-consistent field theory to simulate the microstructure evolution of block copolymer films during SNIPS and find that such films form the desired sponge-like asymmetric porous substructure only if the solvent and nonsolvent have opposite block selectivities and that otherwise they form a dense nonporous microphase-separated film. Our results could have important implications for the choices of solvent and nonsolvent in the processing of block copolymer membranes.

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques.

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques inducing self-rotation, as well as interparticle torques leading to, for instance, the local alignment of particles' orientations. Within this approach, although the functional form of the pairwise interactions does not need to be specified, one can directly map the parameters of the field theory onto the parameters of particle-based models. We perform a linear stability analysis of the homogeneous solution of the field equations and find both long-wavelength and short-wavelength instabilities. The former signals the emergence of a macroscopic structure, which we associate with motility-induced phase separation, while the second one signals the growth of a finite structure with a characteristic size. Intrinsic torques hinder phase separation, pushing the onset of the long-wavelength instability to higher activities. Furthermore, they generate finite-sized structures with a characteristic size proportional to both the self-propulsion velocity and the inverse of the self-rotation frequency. Our results show that a general mechanism might explain why chirality tends to suppress motility-induced phase separation but instead promotes the formation of non-equilibrium patterns.

Spectrum of the hypereclectic spin chain and Pólya counting

In earlier work we proposed a generating function that encodes the Jordan block spectrum of the integrable Hypereclectic spin chain, related to the one-loop dilatation operator of the dynamical fishnet quantum field theory. We significantly improve the expressions for these generating functions, rendering them much more explicit and elegant. In particular, we treat the case of the full spin chain without imposing any cyclicity constraints on the states, as well as the case of cyclic states. The latter involves the Pólya enumeration theorem in conjunction with q-binomial coefficients.

Universality Class of Ising Critical States with Long-Range Losses.

We show that spatial resolved dissipation can act on d-dimensional spin systems in the Ising universality class by qualitatively modifying the nature of their critical points. We consider power-law decaying spin losses with a Lindbladian spectrum closing at small momenta as ∝q^{α}, with α a positive tunable exponent directly related to the power-law decay of the spatial profile of losses at long distances, 1/r^{(α+d)}. This yields a class of soft modes asymptotically decoupled from dissipation at small momenta, which are responsible for the emergence of a critical scaling regime ascribable to the nonunitary counterpart of the universality class of long-range interacting Ising models. For α<1 we find a nonequilibrium critical point ruled by a dynamical field theory described by a Langevin model with coexisting inertial (∼∂_{t}^{2}) and frictional (∼∂_{t}) kinetic coefficients, and driven by a gapless Markovian noise with variance ∝q^{α} at small momenta. This effective field theory is beyond the Halperin-Hohenberg description of dynamical criticality, and its critical exponents differ from their unitary long-range counterparts. Our Letter lays out perspectives for a revision of universality in driven open systems by employing dark states tailored by programmable dissipation.

Formation of diblock copolymer nanoparticles: Theoretical aspects

We explore the shape and internal structure of diblock copolymer (di-BCP) nanoparticles (NPs) by using the Ginzburg-Landau free-energy expansion and the dynamic self-consistent field theory (DSCFT). The self-assembly of di-BCP lamellae confined in emulsion droplets can form either ellipsoidal or onion-like NPs. The corresponding inner structure is a lamellar phase that is either perpendicular to the ellipsoid long axis (L⊥) or forms a multi-layer concentric shell (C∥), respectively. We focus on the effects of the interaction parameters between the A and B monomers χ, and polymer/solvent χPS, as well as the NP size on the nanoparticle shape and internal morphology. The aspect ratio (lAR), defined as the length ratio between the long and short axes, is used to characterize the overall NP shape. Our results show that when the solvent is neutral towards the two blocks, the ratio lAR increases as χ increases, indicating that the NP becomes more elongated. Likewise, decreasing χPS or increasing the NP size also results in a more elongated NP. Furthermore, as the solvent preference towards one of the A or B blocks increases, the NP undergoes a shape transition from a striped ellipsoid (L⊥) to onion-like sphere (C∥). Our results are in good agreement with previous experiments, and some of the predictions could be tested in future experiments.

Brain-inspired multiple-target tracking using Dynamic Neural Fields

Despite considerable progress in the field of automatic multi-target tracking, several problems such as data association remained challenging. On the other hand, cognitive studies have reported that humans can robustly track several objects simultaneously. Such circumstances happen regularly in daily life, and humans have evolved to handle the associated problems. Accordingly, using brain-inspired processing principles may contribute to significantly increase the performance of automatic systems able to follow the trajectories of multiple objects. In this paper, we propose a multiple-object tracking algorithm based on dynamic neural field theory which has been proven to provide neuro-plausible processing mechanisms for cognitive functions of the brain. We define several input neural fields responsible for representing previous location and orientation information as well as instantaneous linear and angular speed of the objects in successive video frames. Image processing techniques are applied to extract the critical object features including target location and orientation. Two prediction fields anticipate the objects’ locations and orientations in the upcoming frame after receiving excitatory and inhibitory inputs from the input fields in a feed-forward architecture. This information is used in the data association and labeling process. We tested the proposed algorithm on a zebrafish larvae segmentation and tracking dataset and an ant-tracking dataset containing non-rigid objects with spiky movements and frequently occurring occlusions. The results showed a significant improvement in tracking metrics compared to state-of-the-art algorithms.

Memory in the relaxation of a polymer density modulation.

Using analytical considerations and particle-based simulations of a coarse-grained model, we study the relaxation of a density modulation in a polymer system without nonbonded interactions. We demonstrate that shallow density modulations with identical amplitudes and wavevectors that have been prepared by different processes exhibit different nonexponential decay behaviors. Thus, in contrast to the popular assumption of dynamic self-consistent field theory, the density alone does not suffice to characterize the configuration of the polymer system. We provide an analytic description within Linear-Response Theory (LRT) and the Rouse model that quantitatively agree with the results of the particle-based simulations. LRT is equivalent to a generalized model-B dynamics with an Onsager coefficient that is nonlocal in space and time. Alternatively, the Rouse description can be cast into a dynamic density-functional theory that uses the full probability distribution of single-chain configurations as a dynamic variable and yields a memory-free description of the dynamics that quantitatively accounts for the dependence on the preparation process. An approximate scheme that only considers the joint distribution of the first two Rouse modes-the ellipsoid model-is also explored.