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We study electric-magnetic duality in Lorentz invariant symmetric tensor gauge theories, where immobile charged particles - fractons - arise due to the generalized current conservation $\partial_μ \partial_ν J^{μν} = 0$ and the fracton gauge principle. We show that the duality in the symmetric gauge theories holds only in four-dimensional spacetime. In higher dimensions, the duality does not hold with only the symmetric gauge fields but tensor fields with more complex symmetries come into play. Furthermore, we show that a hierarchy for the symmetric gauge field theories of higher ranks is interpreted by the bi-form calculus. We also discuss the restricted immobility of $p$-branes in the mixed symmetric gauge theories. As a byproduct, we find that novel self-duality conditions are defined as BPS equations in the four-dimensional Euclidean space.

We propose a framework for parameter estimation in river transport models using breakthrough curve data, which we refer to as Dimensionless Synthetic Transport Estimation (DSTE). We utilize this framework to parameterize the one-dimensional advection-dispersion equation model, incorporating immobile phase exchange through a memory function. We solve the governing equation analytically in the Laplace domain and numerically invert it to generate synthetic breakthrough curves for different memory functions and boundary conditions. A dimensionless formulation enables decoupling the estimation of advection velocity from other parameters, significantly reducing the number of required forward solutions. To improve computational efficiency, we apply a Karhunen-Loeve (KL) expansion to transform the synthetic dataset into a reduced-order space. Given a measured breakthrough curve, we estimate the advection velocity by minimizing the distance from the measurement to the synthetic data in KL space, and infer the remaining dimensionless parameters by Projected Barycentric Interpolation (PBI). We benchmark our method against several alternatives, including Laplace domain fitting, moment matching

We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to establish the uniqueness of this inverse problem. Numerically, we adopt an optimal control approach for determining the source term. A coupled forward-backward system of equations is derived using the first-order optimality condition. Finally, we construct a finite element conjugate gradient algorithm for the numerical inversion of the source term. Several experiments are presented to show the utility of the method.

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Concretely, we obtain that when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the mean squared displacement for immobile tracers when initially all particles are immobile.

We propose an extended compass model that hosts subsystem symmetries and has potential experimental relevance with 3d transition metal compounds. The subsystem symmetries strongly constrain the mobility of spin excitations and lead to profound consequences. At the quantum critical point we find the presence of "critical Bose surface" along the entire $k_x$ and $k_y$ axis. Across which we find a nodal-line spin liquid that undergoes nematic instability at low temperatures. In the ferro-quadrupole phase, we find that one excitation is immobile individually analogous to "fractons".

Adversarial search of a network for an immobile Hider (or target) was introduced and solved for rooted trees by Gal (1979). In this zero-sum game, a Hider picks a point to hide on the tree and a Searcher picks a unit speed trajectory starting at the root. The payoff (to the Hider) is the search time. In Gal's model (and many subsequent investigations), the Searcher receives no additional information after the Hider chooses his location. In reality, the Searcher will often receive such locational information. For homeland security, mobile sensors on vehicles have been used to locate radioactive material stashed in an urban environment. In a military setting, mobile sensors can detect chemical signatures from land mines. In predator-prey search, the predator often has specially attuned senses (hearing for wolves, vision for eagles, smell for dogs, sonar for bats, pressure sensors for sharks) that may help it locate the prey. How can such noisy locational information be used by the Searcher to modify her route? We model such information as signals which indicate which of two branches of a binary tree should be searched first, where the signal has a known accuracy p<1. Our solution

We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random walk models for multi-rate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover we find the associated breakthrough curves, the tracer density at a fixed point in space as function of time, as well as the mobile and immobile concentration profiles and the respective moments of the transport. Specifically we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities transient anomalous transport is observed. Our results have direct applications in geophysical contexts but also in biological, soft matter, and solid state systems.

Cell membranes are anchored to the cytoskeleton via immobile inclusions. We investigate the effect of such anchors on the in-plane dynamics of a fluid membrane and mobile inclusions (proteins) embedded in it. The immobile particles lead to a decreased diffusion coefficient of mobile ones and suppress the correlated diffusion of particle pairs. Due to the long-range, quasi-two-dimensional nature of membrane flows, these effects become significant at a low area fraction (below one percent) of immobile inclusions.

The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower dimensional submanifolds. These so-called "fracton" phases are beyond the usual topological quantum field theory description, and thus require new theoretical frameworks to describe them. Here we consider coupling fracton models to topological quantum field theories in (3+1) dimensions by starting with two copies of a known fracton model and gauging the $\mathbb{Z}_2$ symmetry that exchanges the two copies. This yields a class of exactly solvable lattice models that we study in detail for the case of the X-cube model and Haah's cubic code. The resulting phases host finite-energy non-Abelian immobile quasiparticles with robust degeneracies that depend on their relative positions. The phases also host non-Abelian string excitations with robust degeneracies that depend on the string geometry. Applying the construction to Haah's cubic code in particular provides an exactly solvable model with finite energy yet immobile non-Abelian quasiparticles tha

There have been extensive studies of a random walk among a field of immobile traps (or obstacles), where one is interested in the probability of survival as well as the law of the random walk conditioned on its survival up to time $t$. In contrast, very little is known when the traps are mobile. We will briefly review the literature on the trapping problem with immobile traps, and then review some recent results on a model with mobile traps, where the traps are represented by a Poisson system of independent random walks on ${\mathbb Z}^d$. Some open questions will be given at the end.

We present an analysis of heterogeneous dynamics in molecular dynamics simulations of a thin polymeric film, supported by an absorbing structured surface. Near the glass transition "immobile" domains occur throughout the film, yet the probability of their occurrence decreasing with larger distance from the surface. Still, enough immobile domains are located near the free surface to cause them to percolate in the direction perpendicular to surface, at a temperature near the glass transition temperature. This result is in agreement with a recent theoretical model of glass transition.

The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two regularization algorithms based on the concept of immobile indices and an understanding of the important role these indices play in the feasible sets' characterization. These algorithms are compared to some regularization procedures developed for a more general case of convex problems and based on a facial reduction approach. We show that the immobile-index-based approach combined with the specifics of copositive problems allows us to construct more explicit and detailed regularization algorithms for linear Copositive Programming problems than those already available.

Recent research suggests that the charge carriers in the paramagnetic state of the magnetoresistive manganites are small polarons. Here we report studies of the oxygen-isotope effects on the intrinsic resistivity and thermoelectric power in several ferromagnetic manganites. The precise measurements of these isotope effects allow us to make a quantitative data analysis. Our results do not support a simple small-polaron model, but rather provide compelling evidence for the presence of small immobile bipolarons, i.e., pairs of small polarons. Since the bipolarons in the manganites are immobile, the present result alone appears not to give a positive support to the bipolaronic superconductivity theory for the copper-based perovskites.

We study the behavior of the chemical reactions $A+A\to A+S$ and $A+A\to S+S$ (where the reactive species $A$ and the inert species $S$ are both assumed to be immobile) embedded on Bethe lattices of arbitrary coordination number $z$ and on a two-dimensional (2D) square lattice. For the Bethe lattice case, exact solutions for the coverage in the $A$ species in terms of the initial condition are obtained. In particular, our results hold for the important case of an infinite one-dimensional (1D) lattice ($z=2$). The method is based on an expansion in terms of conditional probabilities which exploits a Markovian property of these systems. Along the same lines, an approximate solution for the case of a 2D square lattice is developed. The effect of dilution in a random initial condition is discussed in detail, both for the lattice coverage and for the spatial distribution of reactants.

The dynamical perspectives of bubble in a liquid droplet on smooth solid substrate can be revealed by investigating interfacial self-assembly phenomena. Moreover, the complexity in such system can be scaled down into a transparent immobile non-Newtonian droplet. Here we present the dynamical approaches of internal microbubbles through coalescence and implosion near the edge of the droplet. The aggregation density of microbubbles near the rim is greater than the central region corresponding to the dynamical behaviour of the droplet marked with capillary flow along the triple phase contact line. We have also numerically analysed the occurrence of aggregation density of internal microbubbles near the edge by implementing boundary integral method. Our numerical results show good agreement with the experimental findings until the aggregation density have occurred near the edge of the droplet. This understanding ascribes distinctive skew exponential power law characteristics through coalescence and implosion.