Diffusion with partial resetting.

Inspired by many examples in nature, stochastic resetting of random processes has been studied extensively in the past decade. In particular, various models of stochastic particle motion were considered where, upon resetting, the particle is returned to its initial position. Here we generalize the model of diffusion with resetting to account for situations where a particle is returned only a fraction of its distance to the origin, e.g., half way. We show that this model always attains a steady-state distribution which can be written as an infinite sum of independent, but not identical, Laplace random variables. As a result, we find that the steady-state transitions from the known Laplace form which is obtained in the limit of full resetting to a Gaussian form, which is obtained close to the limit of no resetting. A similar transition is shown to be displayed by drift diffusion whose steady state can also be expressed as an infinite sum of independent random variables. Finally, we extend our analysis to capture the temporal evolution of drift diffusion with partial resetting, providing a bottom-up probabilistic construction that yields a closed-form solution for the time-dependent distribution of this process in Fourier-Laplace space. Possible extensions and applications of diffusion with partial resetting are discussed.

Structural organization of xanthine crystals in the median ocellus of a member of the ancestral insect group Archaeognatha.

Biogenic purine crystals function in vision as mirrors, multilayer reflectors and light scatterers. We investigated a light sensory organ in a primarily wingless insect, the jumping bristletail Lepismachilis rozsypali (Archaeognatha), an ancestral group. The visual system of this animal comprises two compound eyes, two lateral ocelli, and a median ocellus, which is located on the front of the head, pointing downwards to the ground surface. We determined that the median ocellus contains crystals of xanthine, and we obtained insights into their function. To date, xanthine biocrystals have only been found in the Archaeognatha. We performed a structural analysis, using reflection light microscopy, cryo-FIB-SEM, microCT and cryo-SEM. The xanthine crystals cover the bottom of a bowl-shaped volume in the median ocellus, in analogy to a tapetum, and reflect photons to light-sensitive receptors that are spread in the volume without apparent order or preferential orientation. We infer that the median ocellus operates as an irregular multifocal reflector, which is not capable of forming images. A possible function of this organ is to improve photon capture, and by so doing assess distances from the ground surface when jumping by determining changes in the intensity and contrast of the incident light.

Sample preparation induced phase transitions in solution deposited copper selenide thin films.

Thin films of CuSe were deposited onto GaAs substrate. XRD showed that the as-deposited films were of the Klockmannite (CuSe - P63/mmc 194) phase with lattice parameters a 0 = b 0 = 0.3939 nm, c 0 = 1.7250 nm; however, electron diffraction in the TEM surprisingly indicated the ß-Cu2-x Se phase (Cu1.95Se - R3̄m 166) with lattice parameters a 0 = b 0 = 0.412 nm, c 0 = 2.045 nm. The discrepancy originated from the specimen preparation method, where the energy of the focused ion beam resulted in loss of selenium which drives a phase transition to ß-Cu2-x Se in this system. The same phase transition was observed also upon thermal treatment in vacuum, as well as when the 200 keV electron beam was focused on a powder sample in the TEM. The initial phase can be controlled to some extent by changing the composition of the reactants in solution, resulting in thin films of the cubic α-Cu2-x Se (Cu1.95Se - Fm3̄m) phase co-existing together with the ß-Cu2-x Se phase.

Experimental Realization of Diffusion with Stochastic Resetting.

Stochastic resetting is prevalent in natural and man-made systems, giving rise to a long series of nonequilibrium phenomena. Diffusion with stochastic resetting serves as a paradigmatic model to study these phenomena, but the lack of a well-controlled platform by which this process can be studied experimentally has been a major impediment to research in the field. Here, we report the experimental realization of colloidal particle diffusion and resetting via holographic optical tweezers. We provide the first experimental corroboration of central theoretical results and go on to measure the energetic cost of resetting in steady-state and first-passage scenarios. In both cases, we show that this cost cannot be made arbitrarily small because of fundamental constraints on realistic resetting protocols. The methods developed herein open the door to future experimental study of resetting phenomena beyond diffusion.

Electric Response of CuS Nanoparticle Lubricant Additives: The Effect of Crystalline and Amorphous Octadecylamine Surfactant Capping Layers.

Octadecylamine-coated CuS nanoparticles were designed and confirmed to play an important role in their electric response and boundary lubrication in the ester lubricant. For the case of CuS nanoparticles coated with crystalline surfactant, the surface potential is 18.47 ± 0.99 mV higher than with amorphous surfactant, owing to the random chain conformations of the octadecylamine molecules. When used as a lubricant additive, CuS nanoparticles (in the form of nanoplates or nanoarrays) with a crystalline surfactant were positively charged due to the presence of the amino headgroup in octadecylamine. The observed friction coefficient decreased from 0.18 to 0.09 and 0.05, respectively, when negative potential (for the copper lower pair) was applied across untreated CuS nanoparticles. However, thermally treated CuS nanoparticles showed good lubricating effect, but almost no effect of potential control since the amino groups were obscured by the disordered carbon chains, hindering electron transfer and weakening the response to externally applied electric field.

Surface plasmon resonance in surfactant coated copper sulfide nanoparticles: Role of the structure of the capping agent.

HYPOTHESIS: The optical properties of as-synthesized CuS nanoparticles are affected by shape, size and morphology and exhibit increased optical absorbance in the infrared range due to localized surface plasmon resonance (LSPR), which is also affected by these parameters. An additional parameter which affects the LSPR-related absorbance is crystallinity of the surfactant coating. EXPERIMENTS: CuS nanoparticles with varying morphologies were synthesized using a single source, single surfactant/solvent route. Thereafter, the particles were heat treated at temperatures varying from 130 °C to 230 °C with and without protective environment. Prior to and following the treatments, the particles were characterized using various techniques. Additionally, temperature resolved structural study and thermal analysis of the surfactant coating were performed. FINDINGS: We confirm that the previously reported effects of particle dimensions and chemical composition on LSPR apply for the synthesized particles. Moreover, we report an additional, previously unreported effect, connecting the crystal structure of the nanoparticle surfactant coating to LSPR. This in turn allows control over LSPR peak position by varying the degree of crystallinity of the capping surfactant layer. Thermal study of the surfactant coating showed gradual structural transition and high dependence of phase transformation on atmospheric environment during treatment.