A Convenient Approximation of the Projectile Motion with Quadratic Air Resistance

A convenient approximated analytic solution is proposed for the problem of the motion of a body under a resistive force, acting in the magnitude of the squared velocity of the body. This solution is an explicit function of time, that keeps a good behavior both near the initial state and far from the initial state. To obtain a general analytic solution, we firstly used a reduction principle to be able to manipulate scalar objects, and we analyzed limit behaviors, both near the initial state and far from the initial state. Secondly, we proposed an approximated analytic solution with heuristics based on the built knowledge. Finally, a robust and stable integration scheme is proposed, based on the obtained analytic solution. We compared the scheme with other standard integration schemes.

A numerical survey of nonlinear dynamical responses of discrete pantographic beams

Materials and structures based on pantographic cells exhibit interesting mechanical peculiarities. They have been studied prevalently in the static case, both in linear and nonlinear regime. When the dynamical behavior is considered, available literature is scarce probably for the intrinsic difficulties in the solution of this kind of problems. The aim of this work is to contribute to filling of this gap by addressing the dynamical response of pantographic beams. Starting from a simple spring mechanical model for pantographic beams, the nonlinear equilibrium problem is formulated directly for such a discrete system also considering inertia forces. Successively, the solution of the system of equilibrium equations is sought by means of a stepwise strategy based on a non-standard integration scheme. Here, only harmonic excitations are considered and, for large displacements, frequency-response curves are thoroughly discussed for some significant cases.

Scalable Parallel Manipulation of Single Cells Using Micronozzle Array Integrated with Bidirectional Electrokinetic Pumps

High throughput reconstruction of in vivo cellular environments allows for efficient investigation of cellular functions. If one-side-open multi-channel microdevices are integrated with micropumps, the devices will achieve higher throughput in the manipulation of single cells while maintaining flexibility and open accessibility. This paper reports on the integration of a polydimethylsiloxane (PDMS) micronozzle array and bidirectional electrokinetic pumps driven by DC-biased AC voltages. Pt/Ti and indium tin oxide (ITO) electrodes were used to study the effect of DC bias and peak-to-peak voltage and electrodes in a low conductivity isotonic solution. The flow was bidirectionally controlled by changing the DC bias. A pump integrated with a micronozzle array was used to transport single HeLa cells into nozzle holes. The application of DC-biased AC voltage (100 kHz, 10 Vpp, and VDC: −4 V) provided a sufficient electroosmotic flow outside the nozzle array. This integration method of nozzle and pumps is anticipated to be a standard integration method. The operating conditions of DC-biased AC electrokinetic pumps in a biological buffer was clarified and found useful for cell manipulation.

An Application-Level Method of Arbitrary Synchronization Failure Detection in TTEthernet Networks

Precise distributed clock synchronization is important for Time-Triggered Ethernet (TTEthernet) in which fail-arbitrary synchronization failure cannot be treated by existed protocols unless every synchronization node is equipped with a dedicated clock monitoring. A novel method was presented to detect arbitrary synchronization failure by some application-level routines which make distributed decisions mainly by monitoring the protocol control frames (PCFs). An arbitrary failure node can be exactly detected and located by the routine resided on each of the Compression Masters based on the concerned accusation messages sent from Synchronization Masters or Synchronization Clients. The proposed method can make up the weak points on the detection of the arbitrary failure node of the existed fault-tolerant synchronization mechanism and enhance the synchronization node to resist the arbitrary failure for TTEthernet. By our SAL-based model checking, this method had been formally verified to have a fail-arbitrary detection capacity even in a standard integration configuration. Simulations imply that the quality of the whole clock synchronization is effectively improved after the failure node has been isolated.