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One advantage of a femtosecond laser is that it enables the processing of materials that are otherwise difficult to process via conventional methods such as cutting, grinding, electric discharge machining, etc. However, it is difficult to predict a three dimensional shape processed by the laser. To achieve required three-dimensional shapes using femtosecond lasers with high accuracy and efficiency, it is essential to develop a computer-aided manufacturing (CAM) system that generates processing data (NC data). In this paper, a simulation method is proposed for femtosecond laser processing, which is the basis for the development of a CAM system. A binderless nano-polycrystalline diamond is used as the workpiece material to test the proposed method. Based on a comparison with the experimental results, it is confirmed that the processing shape could be simulated at a high accuracy for fixed-point irradiation as well as scanning irradiation.

In order to achieve high accuracy of computer numerical controlled (CNC) machine tools, various error compensation functions are implemented in the CNC control system. However, these error compensations are not designed to track the dynamic change in accuracies, such as thermal distortion or aging deterioration, during a machining process. To compensate for the dynamic change in accuracy, a built-in automatic measurement and compensation system based on dual linear scales was proposed, and its performance requirement was analyzed. Based on the analysis, a physical prototype was developed, and its feasibility was investigated by a series of experiments. The results showed that the measurement with the linear scale system agreed with a conventional measurement method within the uncertainty estimated at the design stage. In a subsequent experiment, the accuracy compensation was performed based on the measurement value. With compensation, the maximum accuracy deterioration was successfully suppressed from 22 to 3 μm.

Directed energy deposition (DED) is an additive manufacturing (AM) process where a laser is used to fuse a metal powder onto a substrate. The powder is deposited in a layer-by-layer fashion, and each deposited track is referred to as the clad. Large thermal gradients that occur during DED can cause changes in the clad geometry as well as deformation of the substrate and final part. Thermal behavior of DED manufactured parts and mitigation of thermal distortion has been addressed in the literature, but these studies mainly focused on material properties while neglecting the effect of thermal distortion on part geometry. One of the mitigation strategies that has been widely tested and accepted is substrate preheating. This study uses analytical and experimental models to observe changes in clad geometry when energy input to the part is varied by adjusting process parameters and preheating the substrate. A method to quantify substrate energy, or the amount of heat energy the substrate holds, is found as well as a relationship between the substrate energy and clad geometry. The geometry of the clad can be controlled by controlling the total energy added to the clad.

The directed energy deposition (DED) process enables the production of near net shape parts in the starting form of either powder or wire melted by a focused energy source, such as laser. The target geometry is then built layer by layer. In theory, engineering components with complex shapes can be fabricated with a single setup using a hybrid CNC machine tool, which has capabilities of both DED and traditional subtractive machining processes. However, the issue of inaccurate DED deposited geometry and insufficient material deposition results in the repetition of the hybrid process to achieve the goal geometric dimension. This paper presents a generalized strategy for different materials that plan DED toolpath for the planar geometric feature to achieve its required final geometric dimension by using only a single hybrid manufacturing cycle based on simulated results and validate the strategy experimentally by using a hybrid CNC machine.

Calibration of linear encoders has conventionally been performed using an optical interferometer for reference. Calibration using the optical interferometer, however, cannot fulfill the accuracy and stability requirements when the linear encoders exhibit sub-nanometer resolution. This study describes a new calibration method developed using the picometer resolution laser holographic scale as a reference, employing a range-dependent and minimum error-variance algorithm. The method has been evaluated via comparison tests with conventional optical-interferometer-based methods. Moreover, it has also been verified to achieve higher resolution, accuracy, and higher stability during the measurements, even in the atmospheric environment.

Ablation processing using a femtosecond laser has the advantage of processing materials that are impossible to machine by conventional methods. However, it is difficult to predict the three-dimensional removal shape owing to a femtosecond laser irradiation and the current processing method, repeating through trial and error, is inefficient and expensive. For this reason, for processing materials to desired shapes using a femtosecond laser, development of a simulation system and a CAM (Computer-Aided Manufacturing) system are indispensable. In this paper, a simulation method for processing materials using a femtosecond laser is proposed and conducted to nano-polycrystalline diamond (NPD). It is confirmed that the proposed method can precisely simulate the femtosecond laser processing for three-dimensional shape generation. Therefore, the proposed method enables to predict the removal shape identified as the virtual tool shape for calculating a tool path on a CAM system. In addition, an automation process method including an on-machine real-time measurement system of the proposed method is described.

Sapphire capillaries manufactured with high efficiency and precision are needed for use in laser–plasma accelerators. A hybrid manufacturing process combining femtosecond laser machining and diamond tool micromilling was applied. By using a femtosecond laser mounted on a 5-axis machine, a capillary with a groove width of 630 µm and length of 90 mm was fabricated on a sapphire plate within 5 h. The surface roughness of the bottom of the cylinder groove was finished to 7.1 nm in Sa by milling with a polycrystalline diamond end mill.

Inspired by the system of ordinary differential equations in Agusto et al. (2017) that models Zika virus dynamics by taking into account of both sexual and vector-borne transmissions, we furthermore add diffusive terms in order to capture the movement of human hosts and mosquitoes, considering the unique threat of the sexual transmission route of Zika virus. We conduct complete theoretical analysis. In particular, we show that every initial data that is continuous and non-negative admits a unique continuous and non-negative solution for all positive times. Moreover, we derive the basic reproduction number and when it is beneath one, we prove that the disease-free-equilibrium is globally attractive. Finally, when the basic reproduction number is above one, and any of the exposed males or the exposed females or the exposed mosquitoes is not identically zero, we prove the existence of a positive asymptotic lower bound for every component of the solution which in particular implies the uniform persistence of the disease, as well as the existence of at least one positive steady state.

Phenotypic polymorphisms are found in a wide array of taxa, and unravelling the mechanisms that maintain them is of great interest to evolutionary and ecological biologists. Temporal environmental heterogeneity may play a role in the maintenance of polymorphisms but is poorly understood. In the present study, we analysed trends in intergenerational elytral colour morph frequencies in relation to changes in fitness and life history traits (i.e. body size, mortality, fecundity, hatching rate and mate preference) in the ladybird beetle Cheilomenes sexmaculata (Coleoptera: Coccinellidae). A long-term field survey spanning nine years showed that the frequency of dark morphs increases over winter and then decreases in spring. Dark morphs may have an advantage in winter due to their higher tolerance of low temperatures compared with light morphs. Light-morph females were heavier in winter than dark-morph females. They also mated more frequently and had higher hatching rates, potentially causing an increase in light morphs in spring. These results suggest that fluctuations in morph frequencies resulting from the conflicting directions of selection pressures between overwintering and spring generations may help to maintain genetic polymorphism.

The magnetohydrodynamics system consists of the Navier-Stokes equations from fluid mechanics, coupled with the Maxwell’s equations from electromagnetism through multiples of non-linear terms involving derivatives. Following the approach of [1], we prove the existence of a unique invariant measure in case the forcing terms consist of the cylindrical Wiener processes with only low modes. Its proof requires taking advantage of the structure of the non-linear terms carefully and is extended to various other related models such as the magnetohydrodynamics-Boussinesq system from fluid mechanics in atmosphere and oceans, as well as the magneto-micropolar fluid system from the theory of microfluids.

We study the Navier–Stokes equations with a dissipative term that is generalized through a fractional Laplacian in any dimension higher than two. We extend the horizontal Biot–Savart law beyond dimension three. Using the anisotropic Littlewood–Paley theory with which we distinguish the first two directions from the rest, we obtain a blow-up criteria for its solution in norms which are invariant under the rescaling of these equations. The proof goes through for the classical Navier–Stokes equations if dimension is three, four or five. We also give heuristics and partial results toward further improvement

We establish the existence and uniqueness of a local smooth solution to the Cauchy problem for the Hall-magnetohydrodynamics system that is inviscid, resistive, and forced by multiplicative L $$\acute{\mathrm {e}}$$ vy noise in the three dimensional space. Moreover, when the initial data is sufficiently small, we prove that the solution exists globally in time in probability; that is, the probability of the global existence of a unique smooth solution may be arbitrarily close to one given the initial data of which its expectation in a certain Sobolev norm is sufficiently small. The proofs go through for the two and a half dimensional case as well. To the best of the authors’ knowledge, an analogous result is absent in the deterministic case due to the lack of viscous diffusion, exhibiting the regularizing property of the noise. Our result may also be considered as a physically meaningful special case of the extension of work of Kim (J Differ Equ 250:1650–1684, 2011) and Mohan and Sritharan (Pure Appl Funct Anal 3:137–178, 2018) from the first-order quasilinear to the second-order quasilinear system because the Hall term elevates the Hall-magnetohydrodynamics system to the quasilinear class, in contrast to the Naiver–Stokes equations that has most often been studied and is semilinear.

Non-uniqueness of three-dimensional Euler equations and Navier-Stokes equations forced by random noise, path-wise and more recently even in law, have been proven by various authors. We prove non-uniqueness in law of the three-dimensional Navier-Stokes equations forced by random noise and diffused via a fractional Laplacian that has power between zero and one half. The solution we construct has H$\ddot{\mathrm{o}}$lder regularity with a small exponent rather than Sobolev regularity with a small exponent. For the power sufficiently small, the non-uniqueness in law holds at the level of Leray-Hopf regularity. In particular, in order to handle transport error, we consider phase functions convected by not only a mollified velocity field but a sum of that with a mollified Ornstein-Uhlenbeck process if noise is additive and a product of that with a mollified exponential Brownian motion if noise is multiplicative.

A beam delivery system (BDS) fibered with hollow core photonic crystal fibre (HC-PCF) has been identified as very promising for ultra-short pulse (USP) laser micromachining for it allows flexible, secured and robust laser beam delivery to the work piece. These features are of paramount importance for vertical markets such as automotive or consumer electronics. We report on a system that integrates a BDS, a laser beam pointing stabilization module and a 50 W power, 250 fs pulsewidth Yb-based USP laser. The BDS comprises a low loss, low dispersion and high damage threshold Inhibited-Coupling (IC) HC-PCF. The latter is ruggedized with a semi-rigid industrial cable with ends attached respectively to an injection head for ease of laser beam coupling, and to an output connector for beam delivery to the work piece. The injection head is aligned with a special module for laser beam jitter stabilization and beam-shape control and monitoring. Also, it exhibits the necessary gas and thermal handling to minimize parasitic optical nonlinear effect or photoionization and power induced heating. To test the endurance of this fibered-USP laser system, it was continuously run over 17 hours. The results show exceptional integrity in the power transmission (86 ±1%), spectral and temporal structure and beam quality (M2~1.1). The BDS output beam shows a pointing stability of only 0.7±0.1 μrad. These results represent an important milestone towards the industrialization of fiber delivered USP laser-based machines.

Non-uniqueness in law for three-dimensional Navier-Stokes equations forced by random noise was established recently in Hofmanov$\acute{\mathrm{a}}$ et al. (2019, arXiv:1912.11841 [math.PR]). The purpose of this work is to prove non-uniqueness in law for the Boussinesq system forced by random noise. Diffusion within the equation of its temperature scalar field has a full Laplacian and the temperature scalar field can be initially smooth., The range of the exponent of a fractional Laplacian in the 3D case has been expanded. Some other structural changes have been made. This preprint has not undergone peer review or any post-submission improvements or corrections

Laser metal deposition (LMD) is an additive manufacturing technique, whose performance can be influenced by a considerable number of factors and parameters. Typically, a powder is carried by an inert gas and sprayed by a nozzle, with a coaxial laser beam passing through the nozzle and overlapping the powder flow, thereby generating a molten material pool on a substrate. Monitoring the evolution of this process allows for a better comprehension and control of the process, thereby enhancing the deposition quality. As the metal additive manufacturing mechanism has not yet been elucidated, it is not clear how process parameters affect material properties, molding accuracy, and molding efficiency. When cladding is performed under uncertain conditions, a molded part with poor material properties and dimensional accuracy is created. In this paper, we propose a method for high efficiency molding by controlling the distance between the head nozzle and the molten pool in real time. The distance is identified by an originally developed sensor based on a triangulation method. According to the distance, the head nozzle is automatically controlled into the optimum position. As a result, an ideal molding process can be generated, so that high efficiency molding and high-quality material properties can be obtained. Experimental results show that continuing deposition at the optimum distance assists in achieving deposition efficiency and dimensional accuracy. According to the specific experimental results of this method, the modeling efficiency was increased by 27% compared to the method without correction, and the modeling was successful with an error within 1 mm.

We study the two-dimensional Navier-Stokes equations forced by random noise with a diffusive term generalized via a fractional Laplacian that has a positive exponent strictly less than one. Because intermittent jets are inherently three-dimensional, we instead adapt the theory of intermittent form of the two-dimensional stationary flows to the stochastic approach presented by Hofmanov$\acute{\mathrm{a}}$, Zhu $\&$ Zhu (2019, arXiv:1912.11841 [math.PR]) and prove its non-uniqueness in law., arXiv admin note: text overlap with arXiv:2006.11861. This is the version that was accepted by SIAM Journal on Mathematical Analysis (SIMA), before the final edit by the journal

Yamazaki, Kazuo (2018): The Picture of Dorian Gray: shell corrosion allows freshwater and brackish-water gastropods to masquerade as empty shells. Journal of Natural History 52 (35-36): 2331-2338, DOI: 10.1080/00222933.2018.1537408, URL: http://dx.doi.org/10.1080/00222933.2018.1537408

Magnetohydrodynamics system consists of a coupling of the Navier-Stokes and Maxwell's equations and is most useful in studying the motion of electrically conducting fluids. We prove the existence of a unique invariant, and consequently ergodic, measure for the Galerkin approximation system of the three-dimensional magnetohydrodynamics system. The proof is inspired by those of \cite{EM01, R04} on the Navier-Stokes equations; however, computations involve significantly more complications due to the coupling of the velocity field equations with those of magnetic field that consists of four non-linear terms., Comment: This is a pre-print version, and the revised version was accepted by Stochastics: An International Journal of Probability and Stochastic Processes. Its journal reference to be updated later

The ladybird beetle, Menochilus sexmaculatus (Fabricius), has a remarkable elytral colour polymorphism composed of black and red. In the present study, we investigated the effect of temperature on growth from the first instar larva to the pupal stage, as well as maternal morph types on the phenotypic expression of the elytral colour morph in a polymorphic population from Osaka, Japan. Female individuals of three different elytral colour morphs were collected from a wild population, and hatchlings from each female were divided into three groups, which were reared at three constant temperatures: 20 °C, 25 °C, and 30 °C. The phenotypic frequency of F 1 adults indicated that the elytral morph type was determined by genetic factors, but not by growth temperatures. Namely, type A (almost black morph) was the most abundant in F 1 from type A mothers (Male: 52.6%; Female: 32.3%); and types B (four small-dotted morph) and F (four medium-dotted morph) were the most abundant from type B (Male: 56.7%; Female: 53.3%) and type G (four larger-dotted morph) mothers (Male: 33.3%; Female: 31.3%), respectively. Therefore, the expression of elytral colour polymorphism in the Osaka, Japan population is likely to have a genetic basis contingent on parental morphs, rather than a phenotypic plasticity associated with growth temperatures.

Medical screws are a common mass-produced implantable medical component made of Titanium. To machine the threads of these types of components, thread whirling with carbide tools is typically used. However, tool wear and low cutting speed limit the productivity and increase the manufacturing cost of such medical parts. In this study, a direct motor driven thread whirling unit for an advanced Swiss-type CNC lathe was developed and it was used with advanced tool materials such as low binder content Cubic boron nitride (CBN) and Polycrystalline diamond (PCD) to find a cost-effective and more productive alternative to carbide tools.

Micropolar fluid and magneto-micropolar fluid systems are systems of equations with distinctive feature in its applicability and also mathematical difficulty. The purpose of this work is to follow the approach of [ 8 ] and show that another general class of systems of equations, that includes the two-dimensional micropolar and magneto-micropolar fluid systems, is well-posed and satisfies the Laplace principle, and consequently the large deviation principle, with the same rate function.

Repairing, remanufacturing, and refurbishing high value metal components are crucial to move towards a more sustainable economy. Nowadays, repairing operations on high value parts, such as dies, are generally performed using time-consuming manual approaches that rely on the operator’s expertise. The research idea of this paper is to develop a retrofit kit to provide additive capabilities to an existing milling machine, allowing automatic repairing of components thanks to a fast switch between additive and machining operations without a relevant economic investment such the acquisition of a brand-new machine: the final cost of the solution is lower than 10% with respect to the mean cost of a 5-axis milling machine. The additive technology used in this work is Wire Arc Additive Manufacturing (WAAM) that is characterized by a higher deposition rate and a simpler and cost-effective equipment with respect to other techniques (e.g., laser cladding). The design of the system is illustrated in the paper together with the analysis of the results achieved repairing a test case: a die casting mold made of AISI H13 tool steel.

We propose a new mathematical model for cholera transmission dynamics using a system of reaction-convection-diffusion equations. The model differs from previously published partial differential equations (PDEs) based cholera models in that the diffusion and convection processes are only incorporated into the bacterial dynamics, which are described by a general second-order differential operator. This feature allows us to perform a careful study on the movement and dispersal of the pathogenic bacteria in a heterogeneous aquatic environment and its impact on cholera transmission among human hosts. We rigorously analyze the well-posedness and stability of this partially diffusive system, and establish threshold results characterizing cholera transmission dynamics.

Ultra-precision machining of single crystalline sapphire was performed using a polycrystalline diamond (PCD) micro-milling tool. Examination of the machining characteristics indicates that a high-quality surface with a nanometre-scale surface roughness can be obtained when the removed chips are thin enough to achieve ductile-mode machining. Although a high-quality surface was successfully machined, the surface roughness gradually deteriorated and the actual depth of the machined groove became shallower as the machining distance increased because of the build-up of material adhering to the surface of the tool. To retain the milling capabilities of the PCD tool, an electrochemical-assisted surface reconditioning process has been proposed. The reconditioning technique was found to be effective in removing the surface contaminant without causing damage to the edges of the tool.

Differences in the time of occurrence of both sexes of adult ladybirds, which reflect differences in the longevity and reproductive strategies of the sexes, is important from the perspective of applied entomology, including biological control, as well as basic entomology. Nevertheless, there is little field census data on this topic. We investigated the seasonal occurrence of both sexes of Cheilomenes sexmaculata (Fabricius) in Osaka City, central Japan, from 2003 to 2011. Female adults tended to appear earlier than males after hibernation or aestivation. That males never appeared earlier than females during the nine year period of this study indicate that protogyny occurs after hibernation and aestivation in this species.

The theory of micropolar fluids emphasizes the micro-structure of fluids by coupling the Navier–Stokes equations with micro-rotational velocity, and is widely viewed to be well fit, better than the Navier–Stokes equations, to describe fluids consisting of bar-like elements such as liquid crystals made up of dumbbell molecules or animal blood. Following the work of Weinan et al. (Commun Math Phys 224:83–106, 2001), we prove the existence of a unique stationary measure for the stochastic micropolar fluid system with periodic boundary condition, forced by only the determining modes of the noise and therefore a type of finite-dimensionality of micropolar fluid flow. The novelty of the manuscript is a series of energy estimates that is reminiscent from analysis in the deterministic case.

We introduce the stochastic Hall-magneto-hydrodynamics (Hall-MHD) system in three and two and a half dimensions with infinite-dimensional multiplicative noise, white in time, and prove the global existence of a martingale solution via a stochastic Galerkin approximation and applications of Prokhorov’s, Skorokhod’s and martingale representation theorems, as well as the pressure term through de Rham’s theorem adapted to processes. The Hall term represents mathematically a very singular nonlinear term, unprecedented in the previous work. The results extend many others on the deterministic Hall-MHD and stochastic MHD systems and Navier–Stokes equations. In contrast to the stochastic MHD system, the path-wise uniqueness in the two and a half dimensional case is an open problem.

We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in Zhou and Fan (2011). Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in Fan and Ozawa (2009).