Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.     

Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.     

Compressibility of random walker trajectories on growing networks

We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability distribution is bounded as the network size tends to infinity. This means that the growth of a space coupled to a random walker situated in it constrains its dynamics to a set of typical random walker trajectories, and walker trajectories inside the growing space are compressible.     

Partial Oxidation as a Rational Approach to Kinetic Control in Bioinspired Magnetite Synthesis

Biological systems show impressive control over the shape, size and organization of mineral structures, which often leads to advanced physical properties that are tuned to the function of these materials. Such control is also found in magnetotactic bacteria, which produce—in aqueous medium and at room temperature—magnetite nanoparticles with precisely controlled morphologies and sizes that are generally only accessible in synthetic systems with the use of organic solvents and/or the use of high‐temperature methods. The synthesis of magnetite under biomimetic conditions, that is, in water and at room temperature and using polymeric additives as control agents, is of interest as a green production method for magnetic nanoparticles. Inspired by the process of magnetite biomineralization, a rational approach is taken by the use of a solid precursor for the synthesis of magnetite nanoparticles. The conversion of a ferrous hydroxide precursor, which we demonstrate with cryo‐TEM and low‐dose electron diffraction, is used to achieve control over the solution supersaturation such that crystal growth can be regulated through the interaction with poly‐(α,β)‐dl ‐aspartic acid, a soluble, negatively charged polymer. In this way, stable suspensions of nanocrystals are achieved that show remanence and coercivity at the size limit of superparamagnetism, and which are able to align their magnetic moments forming strings in solution as is demonstrated by cryo‐electron tomography.     

Relationship between the spatial position of the seed and growth mode for single-crystal diamond grown with an enclosed-type holder

The relationship between the spatial position of the diamond seed and growth mode is investigated with an enclosed-type holder for single-crystal diamond growth using the microwave plasma chemical vapor deposition epitaxial method. The results demonstrate that there are three main regions by varying the spatial position of the seed. Due to the plasma concentration occurring at the seed edge, a larger depth is beneficial to transfer the plasma to the holder surface and suppress the polycrystalline diamond rim around the seed edge. However, the plasma density at the edge decreases drastically when the depth is too large, resulting in the growth of a vicinal grain plane and the reduction of surface area. By adopting an appropriate spatial location, the size of single-crystal diamond can be increased from 7 mm × 7 mm × 0.35 mm to 8.6 mm × 8.6 mm × 2.8 mm without the polycrystalline diamond rim.     

Reversible Ultra-Slow Crystal Growth of Mixed Lead Bismuth Perovskite Nanocrystals: The Presence of Dynamic Capping

An ultra-slow crystal growth over a period of 24 h of a newly synthesized CH₃NH₃Pb_1/2Bi_1/3I₃ perovskite (MPBI) nanocrystal in non-polar toluene medium is reported here. From several spectroscopic techniques as well as from TEM analysis we found that the size of nanocrystals changes continuously with time, in spite of being capped by the ligands. Using a single molecular spectroscopic technique, we also found that this size change is not due to the stacking of nanocrystals but due to crystal growth. The notable temperature dependence and reversible nature of the nanocrystals growth is explained by the dynamic nature of the capping. The observed temperature-dependent ultra-slow growth is believed to be a pragmatic step towards controlling the size of perovskite NC in a systematic manner.     

Sr3P3N7: Complementary Approach by Ammonothermal and High-Pressure Syntheses

Nitridophosphates exhibit an intriguing structural diversity with different structural motifs, for example, chains, layers or frameworks. In this contribution the novel nitridophosphate Sr₃P₃N₇ with unprecedented dreier double chains is presented. Crystalline powders were synthesized using the ammonothermal method, while single crystals were obtained by a high-pressure multianvil technique. The crystal structure of Sr₃P₃N₇ was solved and refined from single-crystal X-ray diffraction and confirmed by powder X-ray methods. Sr₃P₃N₇ crystallizes in monoclinic space group P2/c. Energy-dispersive X-ray and Fourier-transformed infrared spectroscopy were conducted to confirm the chemical composition, as well as the absence of NH_x functionality. The optical band gap was estimated to be 4.4 eV using diffuse reflectance UV/Vis spectroscopy. Upon doping with Eu²⁺, Sr₃P₃N₇ shows a broad deep-red to infrared emission (λ_em=681 nm, fwhm≈3402 cm⁻¹) with an internal quantum efficiency of 42 %.     

Experimental probes of silver metal nanoparticle formation kinetics: Comparing indirect versus more direct methods

The kinetics of noble metal nanoparticle formation in bottom-up syntheses are important for controlling and optimizing these methods. Hence, experimental probes that are easily accessible to most laboratories are also of interest. We collected kinetic curves for the formation of silver nanoparticles in a modified Turkevich method with citrate acting as the reducing and stabilizing agent by (i) measuring the change in silver nanoparticle surface plasmon resonance by UV-visible spectroscopy, a somewhat indirect method, and then also by (ii) measuring the change in silver ion concentration by ion-selective electrode potentiometry and/or atomic absorption spectroscopy, two more direct methods. The resulting sigmoidal kinetic curves were curvefitted with the Finke-Watzky two-step kinetic model of slow, continuous nucleation and fast autocatalytic growth to extract average rate constants. We found that the kinetic curves obtained by following the change in silver ion concentration were apparent mirror images of those constructed by following the change in nanoparticle surface plasmon resonance, and that their respective curvefits displayed the same sigmoidal characteristics. The resultant values of the rate constants for nucleation and growth overlapped within experimental error between the methods and showed similar trends over the range of citrate concentrations studied. The use of multiple probes in this work to follow the kinetics of nanoparticle formation helps fill a need for the comparison and evaluation of different methods available to scientists, particularly those considered easily accessible.     

Flexible and Epitaxial Metal Oxide Thin Film Growth by Photoreaction Processing for Electrical and Optical Applications

This review summarizes the use of photoreactions that replace conventional heating processes for growing oxide thin films from chemical solutions. In particular, this review outlines key variables in photoreactions that affect epitaxial and polycrystalline thin film growth, including precursor materials, laser wavelength, laser fluence, and carbon. In addition, the features of the photoreaction process that can be controlled at a low temperature by oxygen non-stoichiometry are examined. Likewise, functions that are neither achieved by developing a gradient structure nor controlled by a thermal equilibrium reaction are detailed. Two new concepts are presented, known as photoreaction of nanoparticles (PRNP) and photoreaction of a hybrid solutions (PRHS), in which crystal nuclei are pre-dispersed in a metal–organic compound film. This method has successfully produced flexible phosphor films used as resistor or thermistor electronic components. Finally, thin film growth using different light sources such as flash lamps and femtosecond lasers (fs) is explored.