Numerical Schemes for Stochastic Differential Equations with Variable and Distributed Delays: The Interpolation Approach

A kind of the Euler-Maruyama schemes in discrete forms for stochastic differential equations with variable and distributed delays is proposed. The linear interpolation method is applied to deal with the values of the solutions at the delayed instants. The assumptions of this paper on the coefficients and related parameters are somehow weaker than those imposed by the related past literature. The error estimations for the Euler-Maruyama schemes are given, which are proved to be the same as those for the fundamental EulerMaruyama schemes

Exponential Stability and Numerical Methods of Stochastic Recurrent Neural Networks with Delays

Exponential stability in mean square of stochastic delay recurrent neural networks is investigated in detail. By using Itô’s formula and inequality techniques, the sufficient conditions to guarantee the exponential stability in mean square of an equilibrium are given. Under the conditions which guarantee the stability of the analytical solution, the Euler-Maruyama scheme and the split-step backward Euler scheme are proved to be mean-square stable. At last, an example is given to demonstrate our results

Chemical Micromotors Move Faster at Oil–Water Interfaces

Many real-world scenarios involve interfaces, particularly liquid–liquid interfaces, that can fundamentally alter the dynamics of colloids. This is poorly understood for chemically active colloids that release chemicals into their environment. We report here the surprising discovery that chemical micromotorscolloids that convert chemical fuels into self-propulsionmove significantly faster at an oil–water interface than on a glass substrate. Typical speed increases ranged from 3 to 6 times up to an order of magnitude and were observed for different types of chemical motors and interfaces made with different oils. Such speed increases are likely caused by faster chemical reactions at an oil–water interface than at a glass–water interface, but the exact mechanism remains unknown. Our results provide valuable insights into the complex interactions between chemical micromotors and their environments, which are important for applications in the human body or in the removal of organic pollutants from water. In addition, this study also suggests that chemical reactions occur faster at an oil–water interface and that micromotors can serve as a probe for such an effect

Chemical Micromotors Move Faster at Oil–Water Interfaces

Many real-world scenarios involve interfaces, particularly liquid–liquid interfaces, that can fundamentally alter the dynamics of colloids. This is poorly understood for chemically active colloids that release chemicals into their environment. We report here the surprising discovery that chemical micromotorscolloids that convert chemical fuels into self-propulsionmove significantly faster at an oil–water interface than on a glass substrate. Typical speed increases ranged from 3 to 6 times up to an order of magnitude and were observed for different types of chemical motors and interfaces made with different oils. Such speed increases are likely caused by faster chemical reactions at an oil–water interface than at a glass–water interface, but the exact mechanism remains unknown. Our results provide valuable insights into the complex interactions between chemical micromotors and their environments, which are important for applications in the human body or in the removal of organic pollutants from water. In addition, this study also suggests that chemical reactions occur faster at an oil–water interface and that micromotors can serve as a probe for such an effect

Chemical Micromotors Move Faster at Oil–Water Interfaces

Many real-world scenarios involve interfaces, particularly liquid–liquid interfaces, that can fundamentally alter the dynamics of colloids. This is poorly understood for chemically active colloids that release chemicals into their environment. We report here the surprising discovery that chemical micromotorscolloids that convert chemical fuels into self-propulsionmove significantly faster at an oil–water interface than on a glass substrate. Typical speed increases ranged from 3 to 6 times up to an order of magnitude and were observed for different types of chemical motors and interfaces made with different oils. Such speed increases are likely caused by faster chemical reactions at an oil–water interface than at a glass–water interface, but the exact mechanism remains unknown. Our results provide valuable insights into the complex interactions between chemical micromotors and their environments, which are important for applications in the human body or in the removal of organic pollutants from water. In addition, this study also suggests that chemical reactions occur faster at an oil–water interface and that micromotors can serve as a probe for such an effect

Chemical Micromotors Move Faster at Oil–Water Interfaces

Many real-world scenarios involve interfaces, particularly liquid–liquid interfaces, that can fundamentally alter the dynamics of colloids. This is poorly understood for chemically active colloids that release chemicals into their environment. We report here the surprising discovery that chemical micromotorscolloids that convert chemical fuels into self-propulsionmove significantly faster at an oil–water interface than on a glass substrate. Typical speed increases ranged from 3 to 6 times up to an order of magnitude and were observed for different types of chemical motors and interfaces made with different oils. Such speed increases are likely caused by faster chemical reactions at an oil–water interface than at a glass–water interface, but the exact mechanism remains unknown. Our results provide valuable insights into the complex interactions between chemical micromotors and their environments, which are important for applications in the human body or in the removal of organic pollutants from water. In addition, this study also suggests that chemical reactions occur faster at an oil–water interface and that micromotors can serve as a probe for such an effect