In a smoothly bounded domain $\Omega \subset \mathbb{R}^n$, $n\ge 1$, this manuscript considers the homogeneous Neumann boundary problem for the chemotaxis system

\begin{eqnarray*} \left \{ \begin{array}{l} u_t = \Delta u - \nabla \cdot (u\nabla v), \\[5pt] v_t = \Delta v + u - \alpha uv, \end{array} \right . \end{eqnarray*}

$\alpha \gt 0$

It is shown that there exists $\delta _\star =\delta _\star (n)\gt 0$ such that for any given $\alpha \ge \frac{1}{\delta _\star }$ and for any suitably regular initial data satisfying $v(\cdot, 0)\le \delta _\star$, this problem admits a unique classical solution that stabilizes to the constant equilibrium $(\frac{1}{|\Omega |}\int _\Omega u(\cdot, 0), \, \frac{1}{\alpha })$ in the large time limit.

We consider Gaussian approximation in a variant of the classical Johnson–Mehl birth–growth model with random growth speed. Seeds appear randomly in $\mathbb{R}^d$ at random times and start growing instantaneously in all directions with a random speed. The locations, birth times, and growth speeds of the seeds are given by a Poisson process. Under suitable conditions on the random growth speed, the time distribution, and a weight function $h\;:\;\mathbb{R}^d \times [0,\infty) \to [0,\infty)$, we prove a Gaussian convergence of the sum of the weights at the exposed points, which are those seeds in the model that are not covered at the time of their birth. Such models have previously been considered, albeit with fixed growth speed. Moreover, using recent results on stabilization regions, we provide non-asymptotic bounds on the distance between the normalized sum of weights and a standard Gaussian random variable in the Wasserstein and Kolmogorov metrics.

Loess is a collapsible soil; when it collapses, it can cause significant damage to structures built on it. Improvement in the stability and strength performance of loess is necessary to meet engineering needs. In the present study, the effects on the physical-chemical and rheological characteristics of Ghardaïa loess of adding bentonite and lime (southern Algeria) were examined. Rheological characterization of suspensions was implemented to assess the mechanical sensitivity of the bonds and the structural inter-particle resistance to both the chemical effect and mechanical impact. By analyzing the viscosity results and the evolution of the rheological parameters, the improvements needed in terms of the resistance characteristics of the loess-bentonite and loess-lime mixtures were evaluated and confirmed. The loess physical sensitivity was examined through grain-size distribution and plasticity properties. The pH and electrical conductivity of the mixtures were also used to explore structural modifications. Physical test results showed that introduction of the additives changed the loess texture and improved the plasticity of mixtures. Chemical examination (via change in pH and electrical conductivity) revealed the structural changes in the mixtures studied. Rheological test results showed that increasing concentrations of bentonite and lime improves the mechanical strength and increased the yield stress, consistency, and viscosity of the suspensions. The creation of cement interactions between mixture particles explained the increase in those parameters. Hydration, agglomeration, and inter-particle flocculation induced by the additives promoted these interactions. The experimental results led to the conclusion that bentonite and lime may represent an effective means to improve the performance in terms of preventing loess collapse and to increase its resistance to mechanical impact. The results presented in the present study may provide a geotechnical and rheological working database for the control and treatment of loess collapse and landslides in the region under study. Technical data related to loess may, therefore, be beneficial in terms of civil engineering, public works, hydraulics, and the manufacture of construction materials.

Results of stabilization for the higher order of the Kadomtsev-Petviashvili equation are presented in this manuscript. Precisely, we prove with two different approaches that under the presence of a damping mechanism and an internal delay term (anti-damping) the solutions of the Kawahara–Kadomtsev–Petviashvili equation are locally and globally exponentially stable. The main novelty of this work is that we present the optimal constant, as well as the minimal time, that ensures that the energy associated with this system goes to zero exponentially.

The next generation of high-power lasers enables repetition of experiments at orders of magnitude higher frequency than what was possible using the prior generation. Facilities requiring human intervention between laser repetitions need to adapt in order to keep pace with the new laser technology. A distributed networked control system can enable laboratory-wide automation and feedback control loops. These higher-repetition-rate experiments will create enormous quantities of data. A consistent approach to managing data can increase data accessibility, reduce repetitive data-software development and mitigate poorly organized metadata. An opportunity arises to share knowledge of improvements to control and data infrastructure currently being undertaken. We compare platforms and approaches to state-of-the-art control systems and data management at high-power laser facilities, and we illustrate these topics with case studies from our community.

Signal-to-interference-plus-noise ratio (SINR) percolation is an infinite-range dependent variant of continuum percolation modeling connections in a telecommunication network. Unlike in earlier works, in the present paper the transmitted signal powers of the devices of the network are assumed random, independent and identically distributed, and possibly unbounded. Additionally, we assume that the devices form a stationary Cox point process, i.e., a Poisson point process with stationary random intensity measure, in two or more dimensions. We present the following main results. First, under suitable moment conditions on the signal powers and the intensity measure, there is percolation in the SINR graph given that the device density is high and interferences are sufficiently reduced, but not vanishing. Second, if the interference cancellation factor $\gamma$ and the SINR threshold $\tau$ satisfy $\gamma \geq 1/(2\tau)$ , then there is no percolation for any intensity parameter. Third, in the case of a Poisson point process with constant powers, for any intensity parameter that is supercritical for the underlying Gilbert graph, the SINR graph also percolates with some small but positive interference cancellation factor.

Inverted pendulum systems (IPSs) are mostly used to demonstrate the control rules for keeping the pendulum at a balanced upright position due to a slight force applied to the cart system. This paper presents an application for nonlinear control of an x-z type IPS by using a proportional-integral-derivative (PID) controller with newly established evolutionary tuning method Lightning Search Algorithm (LSA). A single, double and triple PID controller system is tested with the conventional and the self-tuning controllers to get a better understanding of the performance of the given system. The mathematical modelling of the x-z type IPS, the theoretical explanation of the LSA and the simulation analysis of the x-z type IPS is put forward entirely. The LSA algorithm solves the optimization problem of PID controller in an evolutionary way. The most effective way of making comparisons is evaluating the performance results with a well-known optimization technique or with the previous accepted results. We have compared the system’s performance with particle swarm optimization and with a classical control study in the literature. According to the simulation results, LSA-tuned PID controller has the ability to decrease the overshoot better than the conventional-tuned controllers. Finally, it can be concluded that the LSA-supported PID can better stabilize the pendulum angle and track the reference better for non-disturbed and the slightly disturbed systems.

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals arising in stochastic geometry. As a consequence, we provide almost sure central limit theorems for (i) the total edge length of the k-nearest neighbors random graph, (ii) the clique count in random geometric graphs, and (iii) the volume of the set approximation via the Poisson–Voronoi tessellation.

The purpose of this paper is to design a stabilizing controller for a car with n connected trailers. The proposed control algorithm is constructed on the Lyapunov theory. In this paper, the purpose of navigating the system toward the desired point considering the slip phenomenon as a main source of uncertainty is analyzed. First mathematical models are presented. Then, a stabilizing control approach based on the Lyapunov theory is presented. Subsequently, an uncertainty estimator is taken into account to overcome the wheel slip effects. Obtained results show the convergence properties of the proposed control algorithm against the slip phenomenon.

We observe a realization of a stationary weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling technique to construct an unbiased estimator of the average value of this geometric characteristic. Under mild conditions on the weights of the cells, we establish variance asymptotics and the asymptotic normality of the unbiased estimator as the observation window tends to the whole space. Moreover, weak consistency is shown for this estimator.

The United States (US) and Caribbean regions remain vulnerable to the impact of severe tropical storms, hurricanes, and typhoons. In 2017, a series of hurricanes posed threats to residents living in inland and coastal communities as well as on islands isolated from the US mainland. Harvey, Irma, Jose, and Maria caused catastrophic infrastructure damage, resulting in a loss of electrical power and communications due to damaged or downed utility poles, cell towers, and transmission lines. Critical services were inoperable for many months. Emergency managers are public officials who are accountable to both political leaders and the citizens. During disaster events, emergency managers must prioritize areas of effort, manage personnel, and communicate with stakeholders to address critical infrastructure interdependences. Essential lifeline services (eg, energy and communications) were inoperable for many months, which led to increased attention from policy-makers, media, and the public.

This paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.

In this paper we are concerned with the well-posedness and the exponential stabilization of the generalized Korteweg–de Vries–Burgers equation, posed on the whole real line, under the effect of a damping term. Both problems are investigated when the exponent p in the nonlinear term ranges over the interval [1, 5). We first prove the global well-posedness in Hs(ℝ) for 0 ≤ s ≤ 3 and 1 ≤ p < 2, and in H3(ℝ) when p ≥ 2. For 2 ≤ p < 5, we prove the existence of global solutions in the L2-setting. Then, by using multiplier techniques and interpolation theory, the exponential stabilization is obtained with an indefinite damping term and 1 ≤ p < 2. Under the effect of a localized damping term the result is obtained when 2 ≤ p < 5. Combining multiplier techniques and compactness arguments, we show that the problem of exponential decay is reduced to proving the unique continuation property of weak solutions. Here, the unique continuation is obtained via the usual Carleman estimate.

Air pollution control (APC) facilities at waste incinerator plants produce large quantities of solid residues rich in salts and heavy metals. Heavy metals are readily released to water from the residues and it has, therefore, been found suitable to apply a rapid co-precipitation/adsorption process as a means to immobilize the toxic elements. In the ‘Ferrox process’, this immobilization is based on co-precipitation with an Fe(III) oxide formed by oxidation of Fe(II) by air in an aqueous slurry with the APC residue at alkaline pH. In this work we have undertaken a Mössbauer spectroscopy study of the Fe oxide phase formed by precipitation at room temperature and of the oxides present after heating to 600 and 900°C. The only Fe oxide observed in the Ferrox product at room temperature is a very poorly crystalline ferrihydrite. Analytical transmission electron microscopy showed that the main elements associated with the ferrihydrite are Si and Ca. Following heating to 600°C the oxide is still characterized as an amorphous Fe oxide, and it is probable that Si associated with the ferrihydrite is decisive in preventing crystallization. After the 900°C treatment a transformation into defect maghemite is observed. Reducing gases produced from carbon in the samples probably induces this transformation. It eases, thus, the reduction of Fe(III) and the consequent formation of magnetite that eventually oxidizes to maghemite during cooling in air.

The effects of increasing nickel contamination of soil on the update of selected microelements by Brassica juncea L. in the presence of raw halloysite (RH) and halloysite modified by thermal treatment (calcination) at 650°C (MH) were investigated experimentally. Such treatment causes partial dehydroxylation and enhances mineral-adsorption properties towards cations. In a vegetative-pot experiment, four different levels of Ni contamination, i.e. 0 (control), 80, 160, 240 and 320 mg kg−1 were applied in the form of an analytical-grade NiSO4·7H2O solution mixed thoroughly with the soil. Among the minerals which were added to soil to alleviate the negative impact of Ni on plant biomass, MH had a particularly beneficial effect on the growth of B. juncea L. The amount of Ni, Zn, Cu, Mn, Pb and Cr in Indian mustard depended on the Ni dose and type of accompanying mineral structure. The average accumulation of trace elements in B. juncea L. grown in Ni-contaminated soil follow the decreasing order Mn > Zn > Cu > Ni > Pb > Cr.

We study the C*-algebras associated with upper semi-continuous Fell bundles over second-countable Hausdorff groupoids. Based on ideas going back to the Packer–Raeburn ‘stabilization trick’, we construct from each such bundle a groupoid dynamical system whose associated Fell bundle is equivalent to the original bundle. The upshot is that the full and reduced C*-algebras of any saturated upper semi-continuous Fell bundle are stably isomorphic to the full and reduced crossed products of an associated dynamical system. We apply our results to describe the lattice of ideals of the C*-algebra of a continuous Fell bundle by applying Renault's results about the ideals of the C*-algebras of groupoid crossed products. In particular, we discuss simplicity of the Fell-bundle C*-algebra of a bundle over G in terms of an action, described by Ionescu and Williams, of G on the primitive-ideal space of the C*-algebra of the part of the bundle sitting over the unit space. We finish with some applications to twisted k-graph algebras, where the components of our results become more concrete.