Search

We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish the local-in-time existence and uniqueness of mild solutions, and further provide the first result on sharp smoothing effect in analytic space or Gevrey space for soft potentials., Comment: 60pages,0 figure

Living fish may suddenly encounter upstream obstacles, join the queue of the fish schooling, or detect upstream flow in advance, resulting in interactions with environmental vortices that can be abrupt or develop gradually from an initial state. The impact of initial conditions on fish swimming behavior in unsteady upstream vortices remains an open question. This study employs a self-propelled flexible fin model, the immersed boundary method, and direct simulation to analyze the hydrodynamics and locomotion of fish swimming behind a bluff cylinder and within the schooling, under different initial gaps and release styles. Additionally, the above tests were conducted with both quiescent flow fields and fully developed unsteady flows as initial conditions. The results indicate that schooling self-propelled fins are more resilient to initial perturbations compared to fins swimming behind a bluff body. More importantly, when simulations begin with a fully developed wake pattern, which better reflects natural environments, the characteristics of the self-propelled fins remain consistent regardless of the initial release styles. Therefore, from a hydrodynamic perspective, we conclude that initial release styles have limited effects on living fish in unsteady wakes.

We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel combination of the well-explored cancellation mechanism and the idea of linearly-good unknowns, and we use the former idea to deal with the top tangential derivatives and the latter one admitting fast decay rate to control lower-order derivatives., Comment: 33 pages

We present the first theoretical investigation of Fox-Wolfram moments (FWMs) for multi-jet production in relativistic heavy ion collisions. In this work, jet productions in p+p collisions are computed with a Monte Carlo event generator SHERPA, while the Linear Boltzmann Transport model is utilized to simulate the multiple scattering of energetic partons in the hot and dense QCD matter. The event-normalized distributions of the lower-order FWM, $H_1^T$ in p+p and Pb+Pb collisions are calculated. It is found that for events with jet number $n_\text{jet} = 2$ the $H_1^T$ distribution in Pb+Pb is suppressed at small $H_1^T$ while enhanced at large $H_1^T$ region as compared to p+p. For events with $n_\text{jet}>2$, the jet number reduction effect due to jet quenching in the QGP decreases the $H_1^T$ distribution at large $H_1^T$ in Pb+Pb relative to p+p. The medium modification of the Fox-Wolfram moment $H_1^T$ for events with $n_\text{jet}\ge 2$ are also presented, which resemble those of events with $n_\text{jet} = 2$. Its reason is revealed through the relative contribution fractions of events with different final-state jet numbers to $H_1^T$., Comment: 10 pages, 7 figures

We study the hyperbolic version of the Prandtl system derived from the hyperbolic Navier-Stokes system with no-slip boundary condition. Compared to the classical Prandtl system, the quasi-linear terms in the hyperbolic Prandtl equation leads to an additional instability mechanism. To overcome the loss of derivatives in all directions in the quasi-linear term, we introduce a new auxiliary function for the well-posedness of the system in an anisotropic Gevrey space which is Gevrey class $\frac 32$ in the tangential variable and is analytic in the normal variable.

Segmentation of nodules in thyroid ultrasound imaging plays a crucial role in the detection and treatment of thyroid cancer. However, owing to the diversity of scanner vendors and imaging protocols in different hospitals, the automatic segmentation model, which has already demonstrated expert-level accuracy in the field of medical image segmentation, finds its accuracy reduced as the result of its weak generalization performance when being applied in clinically realistic environments. To address this issue, the present paper proposes ASTN, a framework for thyroid nodule segmentation achieved through a new type co-registration network. By extracting latent semantic information from the atlas and target images and utilizing in-depth features to accomplish the co-registration of nodules in thyroid ultrasound images, this framework can ensure the integrity of anatomical structure and reduce the impact on segmentation as the result of overall differences in image caused by different devices. In addition, this paper also provides an atlas selection algorithm to mitigate the difficulty of co-registration. As shown by the evaluation results collected from the datasets of different devices, thanks to the method we proposed, the model generalization has been greatly improved while maintaining a high level of segmentation accuracy.

The electron's charge and spin degrees of freedom are at the core of modern electronic devices. With the in-depth investigation of two-dimensional materials, another degree of freedom, valley, has also attracted tremendous research interest. The intrinsic spontaneous valley polarization in two-dimensional magnetic systems, ferrovalley material, provides convenience for detecting and modulating the valley. In this review, we first introduce the development of valleytronics. Then, the valley polarization forms by the p, d, and f-orbit that are discussed. Following, we discuss the investigation progress of modulating the valley polarization of two-dimensional ferrovalley materials by multiple physical fields, such as electric, stacking mode, strain, and interface. Finally, we look forward to the future developments of valleytronics., Comment: 13 pages, 12 figures Accepted Chinese Physics B (2023) [Invited review]

Quantum batteries are energy storage devices that satisfy quantum mechanical principles. How to obtain analytical solutions for quantum battery systems and achieve a full charging is a crucial element of the quantum battery. Here, we investigate the Rosen-Zener Quantum batteries are energy storage devices that satisfy quantum mechanical principles. How to obtain analytical solutions for quantum battery systems and achieve a full charging is a crucial element of the quantum battery. Here, we investigate the Rosen-Zener quantum battery with $N$ two-level systems, which includes atomic interactions and external driving field. The analytical solutions of the stored energy, changing power, energy quantum fluctuations, and von Neumann entropy (diagonal entropy) are derived by employing the gauge transformation. We demonstrate that full charging process can be achieved when the external driving field strength and scanning period conforms to a quantitative relationship. The local maximum value of the final stored energy corresponds to the local minimum values of the final energy fluctuations and diagonal entropy. Moreover, we find that the atomic interaction induces the quantum phase transition and the maximum stored energy of the quantum battery reaches the maximum value near the quantum phase transition point. Our result provides an insightful theoretical scheme to realize the efficient quantum battery., Comment: 10 pages,7 figures. Accepted in Physical Review A

For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with low regularity, we prove its solutions at any positive time are analytic for strong angular singularity, and in Gevrey class with optimal index for mild angular singularity. To overcome the degeneracy in the spatial variable, a family of well-chosen vector fields with time-dependent coefficients will play a crucial role, and the sharp regularization effect of weak solutions relies on a quantitative estimate on directional derivatives in these vector fields., Comment: 30 pages

Realizing a soft manipulator with biologically comparable flexibility and versatility often requires careful selection of materials and actuation, as well as attentive design of its structure, perception, and control. Here, we report a new class of soft robots (SpiRobs) that morphologically replicates the logarithmic spiral pattern observed in natural appendages (e.g., octopus arms, elephant trunks, etc.). This allows for a common design principle across different scales and a speedy and inexpensive fabrication process. We further present a grasping strategy inspired by the octopus that can automatically adapt to a target object's size and shape. We illustrate the dexterity of SpiRobs and the ability to tightly grasp objects that vary in size by more than two orders of magnitude and up to 260 times self-weight. We demonstrate scalability via three additional variants: a miniaturized gripper (mm), a one-meter-long manipulator, and an array of SpiRobs that can tangle up various objects., Comment: 17 pages, 6 figures

We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index $2$. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator, Comment: 27 pages

We study the spatially inhomogeneous Landau equations with hard potential in the perturbation setting, and establish the analytic smoothing effect in both spatial and velocity variables for a class of low-regularity weak solutions. This shows the Landau equations behave essentially as the hypoelliptic Fokker-Planck operators. The spatial analyticity relies on a new time-average operator, and the proof is based on a straightforward energy estimate with a careful estimate on the derivatives with respect to the new time-average operator., Comment: 43 pages

We consider the hyperbolic version of three-dimensional anisotropic Naver-Stokes equations in a thin strip and its hydrostatic limit that is a hyperbolic Prandtl type equations. We prove the global-in-time existence and uniqueness for the two systems and the hydrostatic limit when the initial data belong to the Gevrey function space with index 2. The proof is based on a direct energy method by observing the damping effect in the systems.

We study the 2D and 3D Prandtl equations of degenerate hyperbolic type, and establish without any structural assumption the Gevrey well-posedness with Gevrey index $\leq 2$. Compared with the classical parabolic Prandtl equations, the loss of the derivatives, caused by the hyperbolic feature coupled with the degeneracy, can't be overcame by virtue of the classical cancellation mechanism that developed for the parabolic counterpart. Inspired by the abstract Cauchy-Kowalewski theorem and by virtue of the hyperbolic feature, we give in this text a straightforward proof, basing on an elementary $L^2$ energy estimate. In particular our argument does not involve the cancellation mechanism used efficiently for the classical Prandtl equations.