Unbounded Channel Research Articles

Random dynamics of stochastic BBM equations driven by nonlinear colored noise on unbounded channel

Random dynamics of stochastic BBM equations driven by nonlinear colored noise on unbounded channel

Existence and uniqueness result for a fluid–structure–interaction evolution problem in an unbounded 2D channel

In an unbounded 2D channel, we consider the vertical displacement of a rectangular obstacle in a regime of small flux for the incoming flow field, modelling the interaction between the cross-section of the deck of a suspension bridge and the wind. We prove an existence and uniqueness result for a fluid–structure-interaction evolution problem set in this channel, where at infinity the velocity field of the fluid has a Poiseuille flow profile. We introduce a suitable definition of weak solutions and we make use of a penalty method. In order to prevent the obstacle from going excessively far from the equilibrium position and colliding with the boundary of the channel, we introduce a strong force in the differential equation governing the motion of the rigid body and we find a unique global-in-time solution.

Hall and ion‐slip effects on MHD natural convective flow past an unbounded vertical porous channel with thermodiffusion

AbstractThe consequences of Soret in addition to Dufour of natural convection heat and mass transfer for the unsteady three‐dimensional boundary layer flow through a perpendicular condition of the existence of viscous dissipation, invariable suction, Hall as well as ion slip consequences into relation. The prevailing partial differential equation is dissolved digitally utilizing the implicit Crank–Nicolson finite difference method. The velocity, temperature, as well as concentration dispensations, is addressed computationally and demonstrated by the graphs. Numerical values of the Nusselt number, skin friction as well as Sherwoods numbers nearby the plate are discussed for a choice of values of substantial parameters and are displayed in a tabular manner. It is noticed that the temperature of the fluid diminishes with higher Prandtl numbers. The resulting velocity diminishes with the growing Hartmann number. Rotation, Soret, and Dufour parameters strengthen the velocity and momentum boundary layer thickness. The velocity intensifies through growing Hall and ion‐slip parameters and the revoke trend is acquired with enhancement in suction parameter.

Magnetic field stabilization of low current DC arc discharge in cross flow in argon gas at atmospheric pressure—a numerical modelling study

In this work we study the effect of an external magnetic field and gas flow on the properties of a low current DC (gliding) arc discharge in argon at atmospheric pressure. We consider a cross flow configuration, in which argon gas flows perpendicularly to the arc current, while the external magnetic field is perpendicular to both the arc current and the gas flow. The study is based on a 2D numerical fluid plasma model of the discharge, coupled with a gas flow model based on the Navier–Stokes equations and a gas thermal balance equation. In the examined configuration, a stabilized arc is achieved by having the E × B drift acting in opposite direction to the gas flow, i.e. the Lorentz force pushing the arc against the gas flow. The numerical model was implemented into a finite element simulation, using the Comsol Multiphysics® (version 5.3) package. The results proved that a magnetically stabilized arc can be sustained and that the examined configuration can be used for effective gas treatment. The analysis of the simulation data helped to answer multiple questions, related to arc stability, the energy density distribution in the arc, and the macroscopic properties of the system as a whole. The results show a significant influence of the walls on the arc stabilization, while in the case of walls positioned very far from the arc, i.e. unbounded channel, the arc becomes a source of a fluid instability, causing vortex shedding. In general, this study provides insight on the interaction between the gas flow and the arc in a strong magnetic field. The model presented here has the potential to further the understanding of magnetically stabilized discharges and to become a basis for developing similar studies of more complex gases.

Relaxed Locally Correctable Codes in Computationally Bounded Channels

Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs between the number of queries the algorithm makes to its oracle (the locality of the task), and the amount of redundancy in the encoding (the information rate). In Hamming's classical adversarial channel model, the current tradeoffs are dramatic, allowing either small locality, but superpolynomial blocklength, or small blocklength, but high locality. However, in the computationally bounded, adversarial channel model, proposed by Lipton (STACS 1994), constructions of locally decodable codes suddenly exhibit small locality and small blocklength, but these constructions require strong trusted setup assumptions e.g., Ostrovsky, Pandey and Sahai (ICALP 2007) construct private locally decodable codes in the setting where the sender and receiver already share a symmetric key. We study variants of locally decodable and locally correctable codes in computationally bounded, adversarial channels, in a setting with no public-key or private-key cryptographic setup. The only setup assumption we require is the selection of the public parameters (seed) for a collision-resistant hash function. Specifically, we provide constructions of relaxed locally correctable and relaxed locally decodable codes over the binary alphabet, with constant information rate, and poly-logarithmic locality. Our constructions, which compare favorably with their classical analogues in the computationally unbounded Hamming channel, crucially employ collision-resistant hash functions and local expander graphs, extending ideas from recent cryptographic constructions of memory-hard functions.

Equilibrium configuration of a rectangular obstacle immersed in a channel flow

Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a Poiseuille flow in an unbounded 2D channel, at least for small Reynolds number and flow rate. We consider both the cases of vertically moving obstacles and obstacles rotating around a fixed pin.

Molecular communication in three-dimensional diffusive channel with mobile nanomachines

A three-dimensional (3-D) diffusive mobile-molecular communication system is considered inside the unbounded environment. We consider a point transmitter and a perfectly absorbing spherical receiver which can move randomly in any of the three coordinates. The closed-form expression for expected hitting rate for 3-D unbounded communication channel with nanomachines mobility is derived. The performance of considered system is further evaluated in terms of probability of detection (PD), probability of false alarm (PFA), and probability of error (Pe). The system is further analyzed in terms of average mutual information and average maximum achievable rate. Furthermore, an optimum decision threshold, at which minimum probability of error and maximum information rate occur is also derived. The analytical results are verified through particle-based and Monte-Carlo simulations.

Resolution of coincident factors in altering the flow dynamics of an MHD elastoviscous fluid past an unbounded upright channel

The influence of simultaneous variation of slip and temperature has been inquired for the case of free-convected flow of an MHD (magnetohydrodynamic), elastoviscous fluid past an unbounded upright plate. How the course of velocity is revamped in response to temperature alterations on boundary has been studied by considering two cases of constant temperature and variable temperature. The inverse and direct role of elastoviscous parameter (K), thermal Grashof number () and Hartmann number (M) in determining the pattern of flow has been discussed through exact expressions and graphical illustrations. Interestingly, a -regime has been identified corresponding to elastoviscous velocity variation. The Newtonian fluid velocity past an unbounded plate entailing slip factor has also been retrieved and compared with elastoviscous fluid velocity. This comparative analysis reflects on magnitude and profile adaptations in response to numerical changes.

Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method

We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel T×R. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity. We also prove a local form of the enhanced viscous dissipation that takes place at times of order ν−1/3, ν being the small viscosity. To prove these results, we use a Hamiltonian approach, following the conjugate operator method developed in the study of Schrödinger operators, combined with a hypocoercivity argument to handle the viscous case.

The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations.

Performance Enriching Channel Allocation Algorithm for Vehicle-to-Vehicle City, Highway and Rural Network.

Future safety applications require the timely delivery of messages between vehicles. The 802.11p has been standardized as the standard Medium Access Control (MAC) protocol for vehicular communication. The 802.11p uses Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) as MAC. CSMA/CA induces unbounded channel access delay. As a result, it induces high collision. To reduce collision, distributed MAC is required for channel allocation. Many existing approaches have adopted Time Division Multiple Access (TDMA) based MAC design for channel allocation. However, these models are not efficient at utilizing bandwidth. Cognitive radio technique is been adopted by various existing approach for channel allocation in shared channel network to maximize system throughput. However, it induces MAC overhead, and channel allocation on a shared channel network is considered to be an NP-hard problem. This work addresses the above issues. Here we present distributed MAC design PECA (Performance Enriching Channel Allocation) for channel allocation in a shared channel network. The PECA model maximizes the system throughput and reduces the collision, which is experimentally proven. Experiments are conducted to evaluate the performance in terms of throughput, collision and successful packet transmission considering a highly congested vehicular ad-hoc network. Experiments are carried out to show the adaptiveness of proposed MAC design considering different environments such City, Highway and Rural (CHR).

Analytical estimation for the impulse response of an n-dimensional diffusion channel with an absorbing receiver

In this letter, we derive an analytic estimate of the impulse response for the n-dimensional unbounded diffusion channel with a spherical absorbing receiver. We use generalized method of images to exploit the hidden phase space symmetries while finding an estimate impulse response for the 2D unbounded channel, for which no exact result exists in the literature. Then, the analytic estimate is compared with effective geometry Monte-Carlo simulations and an error analysis is performed. In particular, a chi-squared analysis is carried out to illustrate the goodness of fit of the estimate. Finally, we propose a second method to derive a nearly exact impulse response with a trade-off of more computation, where the unbounded space is modelled by a bounded space with a far-away ad hoc boundary and the diffusion equation is solved in this finite region.

Molecular Communications: Model-Based and Data-Driven Receiver Design and Optimization

In this paper, we consider a molecular communication system that is made of a 3D unbounded diffusion channel model without flow, a point transmitter, and a spherical absorbing receiver. In particular, we study the impact of inter-symbol interference and analyze the performance of different threshold-based receiver schemes. The aim of this paper is to analyze and optimize the receivers by using the conventional model-based approach, which relies on an accurate model of the system, and the emerging data-driven approach, which, on the other hand, does not need any apriori information about the system model and exploits deep learning tools. We develop a general analytical framework for analyzing the performance of threshold-based receiver schemes, which are suitable to optimize the detection threshold. In addition, we show that data-driven receiver designs yield the same performance as receivers that have perfect knowledge of the underlaying channel model.

Effective Geometry Monte Carlo: A Fast and Reliable Simulation Framework for Molecular Communication

Angular information of messenger molecules absorbed by a receiver plays a significant role in the molecular communication literature. In this paper, we address systematic biases and random errors in the angular information stemming from finite step sizes encountered in traditional simulation frameworks. We show that the effective geometry Monte Carlo (EG-MC) simulation algorithm, which modifies the geometry of the receiver, is a fast and reliable simulation method to overcome these systematic biases. We motivate our approach for a 3-D unbounded diffusion channel consisting of an absorbing receiver and a point transmitter. We show that, with minimal computational cost, the angular distribution of the absorbed particles by the receiver can be precisely obtained using EG-MC algorithm. Afterwards, we demonstrate the accuracy of our simulations and compare them to traditional methods. Then, we comment on the range of applicability of our results. Finally, we consider two simple cases with constant flow and show that the EG-MC algorithm gives consistent results even when the drift is dominant over diffusion. We conclude with further remarks on the computational efficiency and reliability of the EG-MC method.

Analysis and Evaluation of Random Access Transmission for UAV-Assisted Vehicular-to-Infrastructure Communications

In this paper, we propose a random access protocol for vehicular-to-infrastructure communications. We consider the case where an unmanned aerial vehicle (UAV) provides assistance to a roadside unit to enhance the system throughput. In a traditional carrier sense multiple access schemes (CSMA), the vehicle senses the channel first and it does not transmit the data until the channel is free. However, the CSMA has been shown to be often wasteful of resources and includes potentially unbounded channel access delays in dense networks. In this paper, we use the capture effect, where collisions can be resolved, provided the signal-to-interference-plus-noise ratio is larger than a predetermined threshold. Moreover, we show that the access probability of the vehicles can be optimized based on the known density of the network to maximize throughput. Based on the proposed random access protocol, we model the behavior of the vehicles using a two-dimensional Markov chain and derive the expression for the average system throughput. Finally, we propose two transmission power control schemes to further enhance system throughput. We present extensive simulation results to show that the UAV can provide 9%–38% improvement in throughput for variable network densities.

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

The Jin-Neelin model for the El Nino–Southern Oscillation (ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics. From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length k and on each sub-interval to solve successively the oceanic component, using the temperature T calculated on the previous sub-interval, to then solve the sea-surface temperature (SST for short) equation on the current sub-interval. The passage to the limit as k tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.

Benjamin’s gravity current into an ambient fluid with an open surface in a channel of general cross-section

We present the solution of the idealized steady-state gravity current of height $h$ and density $\unicode[STIX]{x1D70C}_{1}$ that propagates into an ambient motionless fluid of height $H$ and density $\unicode[STIX]{x1D70C}_{2}$ in a channel of general non-rectangular cross-section, with an upper surface open to the atmosphere, at high Reynolds number. The current propagates with speed $U$ and causes a depth decrease $\unicode[STIX]{x1D712}$ of the top surface. This is a significant extension of Benjamin’s (J. Fluid Mech., vol. 31, 1968, pp. 209–248) seminal solution for the gravity current in a rectangular (or laterally unbounded) channel with a fixed top ($\unicode[STIX]{x1D712}=0$). The determination of $\unicode[STIX]{x1D712}$ is a part of the problem. Supposing that the direction of propagation is $x$ and gravity acceleration $g$ acts in the $-z$ direction, the sidewalls are specified by $y=-f_{I}(z)$ and $y=f_{II}(z),~z\in [0.H]$, and the width is $f(z)=f_{I}(z)+\,f_{II}(z)$. The dimensionless parameters of the problem are $a=h/H\in (0,1)$ and $r=\unicode[STIX]{x1D70C}_{2}/\unicode[STIX]{x1D70C}_{1}\in (0,1)$. We show that a control-volume analysis of the type used by Benjamin produces a system of algebraic equations for $\tilde{\unicode[STIX]{x1D712}}=\unicode[STIX]{x1D712}/H$ and $Fr=U/(g^{\prime }h)^{1/2}$ as functions of $a$ and $r$, where $g^{\prime }=(r^{-1}-1)g$ is the reduced gravity. The geometry enters the equation via the width function $f(z)$. We present solutions for typical $f(z)$: rectangle, semi-circle, $\vee$ triangle and trapezoid $\text{}\underline{/~\backslash }$ . The results are physically acceptable and insightful. The non-negative dissipation condition defines the domain of validity $a\leqslant a_{max}(r)$ (also depending on $f(z)$); the equality sign corresponds to energy-conserving cases. The critical speed limitation (with respect to the characteristics) is also considered briefly and suggests a slightly smaller $a\leqslant a_{crit}(r)$. The open-top results in the Boussinesq limit $r\rightarrow 1$ coincide with the fixed-top solution. Upon the reduction of $r$, for a fixed thickness $a$, the value of $Fr$ decreases and $\unicode[STIX]{x1D712}$ increases, until the point of energy-conserving (non-dissipative) flow; for smaller $r$, a negative non-physical dissipation appears. The trends are more pronounced for a converging cross-section geometry (like $\text{}\underline{/~\backslash }$ ) than for the opposite shape (like $\vee$ triangle). The previously investigated Benjamin-type steady-state $Fr$ and dissipation results are particular cases of the new formulation: $f(z)=$ const. reproduces the two-dimensional results, and $\unicode[STIX]{x1D712}=0$ recovers the fixed-top solution.

Exact solution of the Muskat–Leibenzon problem for a growing elliptic bubble

The exact solution of the two-phase time-dependent Hele–Shaw problem (in other words, the plane Muskat–Leibenzon problem) in which a fluid occupied an unbounded channel is displaced by another fluid incoming through a slitted cut in the channel. In this case the interface between the phases, namely, fluids of different viscosity, evolves as an ellipse whose area and eccentricity vary continuously.

Online Power Control Optimization for Wireless Transmission with Energy Harvesting and Storage

We consider wireless transmission over fading channel powered by energy harvesting and storage devices. Assuming a finite battery storage capacity, we design an online power control strategy aiming at maximizing the long-term time-averaged transmission rate under battery operational constraints for energy harvesting. We first formulate the stochastic optimization problem, and then develop techniques to transform this problem and employ techniques from Lyapunov optimization to design the online power control solution. In particular, we propose an approach to handle unbounded channel fade which cannot by directly dealt with by Lyapunov framework. Our proposed algorithm determines the transmission power based only on the current energy state of the battery and channel fade conditions,without requiring any knowledge of the statistics of energy arrivals and fading channels. Our online power control solution is a three-stage closed-form solution depending on the battery energy level. It not only provides strategic energy conservation through the battery energy control, but also reveals an opportunistic transmission style based on fading condition, both of which improve the long-term time-averaged transmission rate. We further characterize the performance bound of our proposed algorithm to the optimal solution with a general fading distribution. Simulation results demonstrate a significant performance gain of our proposed online algorithm over alternative online approaches.

On Reachability for Unidirectional Channel Systems Extended with Regular Tests

"Unidirectional channel systems" (Chambart & Schnoebelen, CONCUR 2008) are finite-state systems where one-way communication from a Sender to a Receiver goes via one reliable and one unreliable unbounded fifo channel. While reachability is decidable for these systems, equipping them with the possibility of testing regular properties on the contents of channels makes it undecidable. Decidability is preserved when only emptiness and nonemptiness tests are considered: the proof relies on an elaborate reduction to a generalized version of Post's Embedding Problem.