Smoothing effects for classical solutions of the relativistic Landau–Maxwell system

AbstractThe relativistic Landau–Maxwell system is one of the most fundamental and complete models for describing the dynamics of a dilute hot plasma in which particles interact through Coulomb collisions and their self-consistent electromagnetic field. In this work, we prove that the classical solutions obtained by Strain and Guo become immediately smooth with respect to all variable under the extra assumption of the electromagnetic field. As a by-product, we also prove that the classical solutions to the relativistic Landau–Poisson system and the relativistic Landau equation have the same property without any extra assumption

The Crystal Structure of Monovalent Streptavidin.

The strong interaction between streptavidin (SA) and biotin is widely utilized in biotechnological applications. A SA variant, monovalent SA, was developed with a single and high affinity biotin-binding site within the intact tetramer. However, its structural characterization remains undetermined. Here, we seek to determine the crystal structure of monovalent SA at 1.7-Å resolution. We show that, in contrast to its 'close-state' in the only wild-type subunit, the L3,4 loops of three Dead SA subunits are free from crystal packing and remain in an 'open state', stabilized by a consistent H-bonding network involving S52. This H-bonding network also applies to the previously reported open state of the wild-type apo-SA. These results suggest that specific substitutions (N23A/S27D/S45A) at biotin-binding sites stabilize the open state of SA L3,4 loop, thereby further reducing biotin-binding affinity. The general features of the 'open state' SA among different SA variants may facilitate its rational design. The structural information of monovalent SA will be valuable for its applications across a wide range of biotechnological areas

Global classical solutions to the initial value problem for the relativistic Landau equation

AbstractGlobal in time classical solutions near the relativistic Maxwellian are constructed for the relativistic Landau equation in the whole space. The construction of global solutions is based on refined energy analysis

Does Notch play a tumor suppressor role across diverse squamous cell carcinomas?

The role of Notch pathway in tumorigenesis is highly variable. It can be tumor suppressive or pro-oncogenic, typically depending on the cellular context. Squamous cell carcinoma (SCC) is a cancer of the squamous cell, which can occur in diverse human tissues. SCCs are one of the most frequent human malignancies for which the pathologic mechanisms remain elusive. Recent genomic analysis of diverse SCCs identified marked levels of mutations in NOTCH1, implicating Notch signaling pathways in the pathogenesis of SCCs. In this review, evidences highlighting NOTCH's role in different types of SCCs are summarized. Moreover, based on accumulating structural information of the NOTCH receptor, the functional consequences of NOTCH1 gene mutations identified from diverse SCCs are analyzed, emphasizing loss of function of Notch in these cancers. Finally, we discuss the convergent view on an intriguing possibility that Notch may function as tumor suppressor in SCCs across different tissues. These mechanistic insights into Notch signaling pathways will help to guide the research of SCCs and development of therapeutic strategies for these cancers

Asymptotics toward viscous contact waves for solutions of the Landau equation

In the paper, we are concerned with the large time asymptotics toward the viscous contact waves for solutions of the Landau equation with physically realistic Coulomb interactions. Precisely, for the corresponding Cauchy problem in the spatially one-dimensional setting, we construct the unique global-in-time solution near a local Maxwellian whose fluid quantities are the viscous contact waves in the sense of hydrodynamics and also prove that the solution tends toward such local Maxwellian in large time. The result is proved by elaborate energy estimates and seems the first one on the dynamical stability of contact waves for the Landau equation. One key point of the proof is to introduce a new time-velocity weight function that includes an exponential factor of the form $\exp (q(t)\langle \xi\rangle^2)$ with $$q(t):=q_1-q_2\int_0^tq_3(s)\,ds,$$ where $q_1$ and $q_2$ are given positive constants and $q_3(\cdot)$ is defined by the energy dissipation rate of the solution itself. The time derivative of such weight function is able to induce an extra quartic dissipation term for treating the large-velocity growth in the nonlinear estimates due to degeneration of the linearized Landau operator in the Coulomb case. Note that in our problem the explicit time-decay of solutions around contact waves is unavailable but no longer needed under the crucial use of the above weight function, which is different from the situation in [11, 14].Comment: 60 pages. Comments are most welcome. Slight modifications have been made to simplify some estimates using the conservation of mas

KdV limit for the Vlasov-Poisson-Landau system

Two fundamental models in plasma physics are given by the Vlasov-Poisson-Landau system and the compressible Euler-Poisson system which both capture the complex dynamics of plasmas under the self-consistent electric field interactions at the kinetic and fluid levels, respectively. Although there have been extensive studies on the long wave limit of the Euler-Poisson system towards Korteweg-de Vries equations, few results on this topic are known for the Vlasov-Poisson-Landau system due to the complexity of the system and its underlying multiscale feature. In this article, we derive and justify the Korteweg-de Vries equations from the Vlasov-Poisson-Landau system modelling the motion of ions under the Maxwell-Boltzmann relation. Specifically, under the Gardner-Morikawa transformation $$(t,x,v)\to (\delta^{\frac{3}{2}}t,\delta^{\frac{1}{2}}(x-\sqrt{\frac{8}{3}}t),v)$$ with $\varepsilon^{\frac{2}{3}}\leq \delta\leq \varepsilon^{\frac{2}{5}}$ and $\varepsilon>0$ being the Knudsen number, we construct smooth solutions of the rescaled Vlasov-Poisson-Landau system over an arbitrary finite time interval that can converge uniformly to smooth solutions of the Korteweg-de Vries equations as $\delta\to 0$. Moreover, the explicit rate of convergence in $\delta$ is also obtained. The proof is obtained by an appropriately chosen scaling and the intricate weighted energy method through the micro-macro decomposition around local Maxwellians.Comment: 68 pages. All comments are welcome. arXiv admin note: text overlap with arXiv:2212.0765

国际社会应共同努力建立基于新规则的新秩序

In its nature, world history is an evolutionary cycle of non-rules, non-order to rules and order. The Peace of Westphalia began the international order aiming to resolve disputes through multinational meetings. However, the fragile world order and the code of international relations failed to prevent World War Ⅰ. Although a new system of multinational mechanisms, formed after World War I, reformed the international community, it did not stop World War Ⅱ from breaking out. After World War Ⅱ, a new system of international organizations represented by the United Nations and new norms of international relations centered on the Charter of the United Nations were established. Despite its undeniable role in the world order and the norms of international relations, the so-called Yalta System, still has its flaws. After the end of the Cold War, the necessity of a new world political, economic and security order is rising. The theory and practice of global governance is in need of upgrading. However, due to complicated historical and realistic reasons, the process of building up a new order based on new rules would be long and tortuous. Key Words: International Order, Power Relations, Charter of the United Nations, Global Governance世界历史归根到底，就是从无规则无秩序到有规则有秩序，再到建立新规则新秩序无限发展历程。威斯特伐利亚条约的诞生，标志着以多边会议为争端解决机制的国际秩序开始形成，但粗陋而孱弱的世界秩序和国际关系准则并没能阻止第一次世界大战的爆发。一战后形成的一系列新型多边合作机制曾使国际社会欢欣鼓舞，但这套体制和规则仍未能阻止二战的爆发。国际社会于二战结束之际，建立起以联合国为代表的新的国际组织体系和联合国宪章为核心的新型国际关系准则。这套名为雅尔塔体系的世界秩序和国际关系规则虽然发挥了不可否认的历史作用，但许多方面仍不尽如人意。冷战结束后，世界呼唤新的政治经济秩序、安全格局，全球治理从理论到实践都亟待更新。但由于极其复杂的历史和现实原因，建立基于新规则的新秩序，将是一个漫长而曲折的历史过程。 【关键词】国际秩序，大国关系，联合国宪章，全球治

Formation Control of Localised and Decentralised Robotic Swarms

Robot swarms consist of multiple autonomous robots, which detect and interact with their local environments. The fundamental intelligence is observed when a chaotic swarm reaches a stable and orderly objective formation. The process is important because the objective formation is designed such that the swarm achieves more than the sum of its individuals. A formation is a set of positions or tasks, and intelligent swarms are capable of self-organising and task allocating. Given an objective formation, individuals of a swarm reach different objective positions and perform different tasks. This implies task allocation in different possible choices. For each individual, the path to its objective position is regarded as the efort to take, and the inclination to different objective tasks means different eforts. The challenge is that it needs to choose wisely in the interaction with its neighbourhood. Changes of choices are compromises and each progress to the objective position imposes in uence on its neighbourhood. The collective intelligence comes from series of individual decisions in the process. In this thesis, we consider four problems that arise with the challenge. We use techniques from graph theory and agent-based design to address them. Formation control algorithms should not impose heavy burden in the communication network. Thus, to start with, limited sensing and communication are assumed, and the robots have minimal access to each other's identity through locally established channels. The control strategy is proposed based on local optimisation and multi-object mapping for a team of robots. Robots are able to make mapping decisions based on local information. To achieve the local optimal mapping decisions for each robot, two novel multi-object mapping protocols are designed. The first protocol performs confict locating and resolving, and the second adopts a most-neighbour mapping strategy. The formation problem is further addressed for a scalable team of robots subject to limited sensing with no communication. The robots themselves are fully independent with no designated roles. Scalable objective formation design is proposed such that the robot formation is scalable. Under the assumption that the data transmission among the robots is not available, a novel controller and a protocol are designed that do not rely on communication. As the controller only drives the robots to a partially desired formation, a distributed coordination protocol is proposed to resolve the imperfections. The case is investigated where the objective formations are arbitrary and have fixed sizes. Multi-objective mapping is proposed for the individual robots to identify their positions in the objective formation. The fixed formation size induces mapping loops, and to avoid local optimum traps, an evaluation method imposes a weak restriction on the predened formation, rendering it almost arbitrary. To enhance the robustness, the minimal local topology is proposed, and to reduce the computation burden and avoid the infnite trajectory loop, the coordination protocol is modifed by introducing probability. The practical problem of collision avoidance is also studied. The leaderfollower scheme is implemented on a multi-robot platform. On the premise of coordinated control laws, globally desired formation is achieved. The same problem in the path-planning perspective is considered on a global scale. Disc obstacles are filtered and clusters are identified based on their intersections. The path planning algorithm is designed based on obstacle clusters.Thesis (Ph.D.) -- University of Adelaide, School of Electrical & Electronic Engineering, 201