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Control of frictional interactions among liquid-suspended particles has led to tunable, strikingly non-Newtonian rheology via the formation of strong flow constraints as particles come into close proximity under shear. Typically, these frictional interactions have been in the form of physical contact, controllable via particle shape and surface roughness. We investigate a different route, where molecular bridging between nearby particle surfaces generates a controllable "sticky" friction. This is achieved with surface-functionalized colloidal particles capable of forming dynamic covalent bonds with telechelic polymers that comprise the suspending fluid. At low shear stress this results in particles coated with a uniform polymer brush layer. Beyond an onset stress the telechelic polymers become capable of bridging and generate shear thickening. Over the size range investigated, we find that the dynamic brush layer leads to dependence of the onset stress on particle diameter that closely follows a power law with exponent -1.76. In the shear thickening regime, we observe an enhanced dilation in measurements of the first normal stress difference and reduction in the extrapolated volume fraction required for jamming, both consistent with an effective particle friction that increases with decreasing particle diameter. These results are discussed in light of predictions for suspensions of hard spheres and of polymer-grafted particles.

Zagier-Hoffman's conjectures predict the dimension and a basis for the $\mathbb Q$-vector spaces spanned by $N$th cyclotomic multiple zeta values (MZV's) of fixed weight where $N$ is a natural number. For $N=1$ (MZV's case), half of these conjectures have been solved by the work of Terasoma, Deligne-Goncharov and Brown with the help of Zagier's identity. The other half are completely open. For $N=2$ (alternating MZV's case) and $N=3,4,8$, Deligne-Goncharov and Deligne solved the same half of these conjectures for $N$th-cyclotomic MZV's. For other values of $N$, no sharp upper bound on the dimension is known. In this paper we completely establish, for all $N$, Zagier-Hoffman's conjectures for $N$th cyclotomic multiple zeta values in positive characteristic. By working with the tower of all cyclotomic extensions, we present a proof that is uniform on $N$ and give an effective algorithm to express any cyclotomic multiple zeta value in the chosen basis. This generalizes all previous work on these conjectures for MZV's and alternating MZV's in positive characteristic., Comment: 45 pages

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify their effectiveness in the mesh-free framework of PINNs, which allows automated construction of virtual representation without manual mesh generation. Then, the overall performance of the data-driven PINNs (DD-PINNs) framework is examined, which can utilize the acquired datasets in DT scenarios. Its scalability to more general physics is validated within parametric Navier-Stokes equations, where PINNs do not need to be retrained as the Reynolds number varies. In addition, since datasets can be often collected from different fidelity/sparsity in practice, multi-fidelity DD-PINNs are also proposed and evaluated. They show remarkable prediction performance even in the extrapolation tasks, with $42\sim62\%$ improvement over the single-fidelity approach. Finally, the uncertainty quantification performance of multi-fidelity DD-PINNs is investigated by the ensemble method to verify their potential in DT, where an accurate measure of predictive uncertainty is critical. The DD-PINN frameworks explored in this study are found to be more suitable for DT scenarios than traditional PINNs from the above perspectives, bringing engineers one step closer to seamless DT realization.

Data-driven surrogate modeling has surged in capability in recent years with the emergence of graph neural networks (GNNs), which can operate directly on mesh-based representations of data. The goal of this work is to introduce an interpretable fine-tuning strategy for GNNs, with application to unstructured mesh-based fluid dynamics modeling. The end result is an enhanced fine-tuned model that isolates regions in physical space, corresponding to sub-graphs, that are intrinsically linked to the forecasting task while retaining the predictive capability of the baseline. These structures, identified by the fine-tuned GNNs, are adaptively produced in the forward pass and serve as explainable links between the baseline model architecture, the optimization goal, and known problem-specific physics. Additionally, through a regularization procedure, the fine-tuned GNNs can also be used to identify, during inference, graph nodes that correspond to a majority of the anticipated forecasting error, adding a novel interpretable error-tagging capability to baseline models. Demonstrations are performed using unstructured flow field data sourced from flow over a backward-facing step at high Reynolds numbers, with geometry extrapolations demonstrated for ramp and wall-mounted cube configurations.

In \cite{IKLNDP23} we presented a systematic study of algebra structures of multiple zeta values in positive characteristic introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we construct algebra and Hopf algebra structures of alternating multiple zeta values introduced by Harada, extending our previous work. Our results could be considered as an analogue of those of Hoffman \cite{Hof00} and Racinet \cite{Rac02} in the classical setting. The proof is based on two new ingredients: the first one is a direct and explicit construction of the shuffle Hopf algebra structure, and the second one is the notion of horizontal maps., Comment: 37 pages. arXiv admin note: text overlap with arXiv:2301.05906

In this paper, we present offline-to-online knowledge distillation (OOKD) for video instance segmentation (VIS), which transfers a wealth of video knowledge from an offline model to an online model for consistent prediction. Unlike previous methods that having adopting either an online or offline model, our single online model takes advantage of both models by distilling offline knowledge. To transfer knowledge correctly, we propose query filtering and association (QFA), which filters irrelevant queries to exact instances. Our KD with QFA increases the robustness of feature matching by encoding object-centric features from a single frame supplemented by long-range global information. We also propose a simple data augmentation scheme for knowledge distillation in the VIS task that fairly transfers the knowledge of all classes into the online model. Extensive experiments show that our method significantly improves the performance in video instance segmentation, especially for challenging datasets including long, dynamic sequences. Our method also achieves state-of-the-art performance on YTVIS-21, YTVIS-22, and OVIS datasets, with mAP scores of 46.1%, 43.6%, and 31.1%, respectively.

Multiples zeta values (MZV's for short) in positive characteristic were introduced by Thakur as analogues of classical multiple zeta values of Euler. In this paper we give a systematic study of algebraic structures of MZV's in positive characteristic. We construct both the stuffle algebra and the shuffle algebra of these MZV's and equip them with algebra and Hopf algebra structures. In particular, we completely solve a problem suggested by Deligne and Thakur \cite{Del17} in 2017 and establish Shi's conjectures \cite{Shi18}. The construction of the stuffle algebra is based on our recent work \cite{IKLNDP22}., Comment: 116 pages

In this paper, we study common zeros of the iterated derivatives of the Eisenstein series for $\Gamma_0^+(N)$ of level $N=1,2$ and $3$, which are quasi-modular forms. More precisely, we investigate the common zeros of quasi-modular forms, and prove that all the zeros of the iterated derivatives of the Eisenstein series $\frac{d^m E_k^{(N)}(\tau)}{d\tau^m}$ of weight $k=2,4,6$ for $\Gamma_0^+(N)$ of level $N=2,3$ are simple by generalizaing the results of Meher \cite{MEH} and Gun and Oesterl\'{e} \cite{SJ20} for SL$_2(\mathbb{Z})$., Comment: 23 pages, 1 figure

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear relations among alternating multiple zeta values and settle the main goals of these theories. As a consequence we completely establish Zagier-Hoffman's conjectures in positive characteristic formulated by Todd and Thakur which predict the dimension and an explicit basis of the span of multiple zeta values of Thakur of fixed weight., Comment: 60 pages (the details of proofs have been added)

The non-Newtonian behaviors of dense suspensions are central to their use in technological and industrial applications and arise from a network of particle-particle contacts that dynamically adapts to imposed shear. Reported herein are studies aimed at explor-ing how dynamic covalent chemistry between particles and the polymeric solvent can be used to tailor such stress-adaptive contact networks leading to their unusual rheological behaviors. Specifically, a room temperature dynamic thia-Michael bond is employed to rationally tune the equilibrium constant (Keq) of the polymeric solvent to the particle interface. It is demonstrated that low Keq leads to shear thinning while high Keq produces antithixotropy, a rare phenomenon where the viscosity increases with shearing time. It is proposed that an increase in Keq increases the polymer graft density at the particle surface and that antithixotropy primar-ily arises from partial debonding of the polymeric graft/solvent from the particle surface and the formation of polymer bridges between particles. Thus, the implementation of dynamic covalent chemistry provides a new molecular handle with which to tailor the macroscopic rheology of suspensions by introducing programable time dependence. These studies open the door to energy absorbing materials that not only sense mechanical inputs and adjust their dissipation as a function of time or shear rate but can switch between these two modalities on demand., Comment: 9 pages, 5 figures (Supporting: 26 pages, 17 figures)