Transfer function models for distributed-parameter systems with impedance boundary conditions

Rabenstein, Rudolf; Schäfer, Maximilian; Strobl, Christian

doi:10.1080/00207179.2017.1397753

Cited by 9 publications

(41 citation statements)

References 16 publications

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“…Before the transfer function model for the considered diffusion process is constructed in Section III, the auxiliary PDE in (6a), (6b), the boundary conditions (6c), and the initial conditions (6d) are rearranged into a unified vector form according to [15]. The reformulation of the PDE in (6a), (6b) in terms of a matrix valued spatial differential operator L defined on the circular disk…”

Section: Vector Formulationmentioning

confidence: 99%

“…Index µ ∈ Z is the index of a spatial frequency variable s µ,n for which (7) has nontrivial solutions [14], [15]. Both sets of eigenfunctions K n andK n are determined from problem-specific eigenvalue problems [15]. The index n ∈ Z is here already introduced because of the Bessel-nature of the eigenfunctions, cf.…”

Section: A Transfer Function Modelmentioning

confidence: 99%

“…3) Eigenfunctions and Eigenfrequencies: The eigenfunctions for the forward and inverse transformation are derived by solving a dedicated eigenvalue problem [14]. Its derivation is skipped here for brevity but it is described for similar problems in [15], [21]. The eigenfunctions in (13), (14) are obtained as…”

Section: A Transfer Function Modelmentioning

confidence: 99%

“…The goal is an expression forΦ n (µ, s) in terms of the state vector Y (s) of the state-space description. A feedback matrix for the system is constructed according to the concepts described in [15]. The starting point is the general transformed boundary term (17).…”

Section: B Feedback Loopmentioning

confidence: 99%

“…This technique has been already applied successfully, e.g. in the field of sound synthesis and circuit modeling, see [15], [16] for further references. This kind of modeling technique offers several benefits: It leads to semi-analytical models in terms of a statespace description which provide insights into the diffusion process.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

Schäfer

Wicke

Rabenstein

et al. 2019

ICC 2019 - 2019 IEEE International Conference on Communications (ICC)

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This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or magnetism. The dynamics of the diffusion process are modeled by multi-dimensional transfer functions in a spatio-temporal frequency domain. Realistic boundary conditions are incorporated by the design of a feedback loop. The result is a discretetime semi-analytical model for the particle concentration in the channel. The model is validated by comparison to particlebased simulations. These numerical experiments reveal that the particle concentration of the proposed semi-analytical model and the particle-based model are in excellent agreement. The analytical form of the proposed solution provides several benefits over purely numerical models, e.g. high flexibility, existence of low run-time algorithms, extendability to several kinds of boundary conditions, and analytical connection to parameters from communication theory.

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Section: Vector Formulationmentioning

confidence: 99%

Section: A Transfer Function Modelmentioning

confidence: 99%

Section: A Transfer Function Modelmentioning

confidence: 99%

Section: B Feedback Loopmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

Schäfer

Wicke

Rabenstein

et al. 2019

ICC 2019 - 2019 IEEE International Conference on Communications (ICC)

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Cooperative optimization techniques in distributed MAC protocols – a survey

Subramanyam,

Jancy,

Nagabushanam

2023

IJPCC

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Purpose Cross-layer approach in media access control (MAC) layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in wireless sensor network (WSN) and Internet of Things (IoT) applications. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes. Game theory optimization for distributed may increase the network performance. The purpose of this study is to survey the various operations that can be carried out using distributive and adaptive MAC protocol. Hill climbing distributed MAC does not need a central coordination system and location-based transmission with neighbor awareness reduces transmission power. Design/methodology/approach Distributed MAC in wireless networks is used to address the challenges like network lifetime, reduced energy consumption and for improving delay performance. In this paper, a survey is made on various cooperative communications in MAC protocols, optimization techniques used to improve MAC performance in various applications and mathematical approaches involved in game theory optimization for MAC protocol. Findings Spatial reuse of channel improved by 3%–29%, and multichannel improves throughput by 8% using distributed MAC protocol. Nash equilibrium is found to perform well, which focuses on energy utility in the network by individual players. Fuzzy logic improves channel selection by 17% and secondary users’ involvement by 8%. Cross-layer approach in MAC layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in WSN and IoT applications. Cross-layer and cooperative communication give energy savings of 27% and reduces hop distance by 4.7%. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes. Research limitations/implications Other optimization techniques can be applied for WSN to analyze the performance. Practical implications Game theory optimization for distributed may increase the network performance. Optimal cuckoo search improves throughput by 90% and reduces delay by 91%. Stochastic approaches detect 80% attacks even in 90% malicious nodes. Social implications Channel allocations in centralized or static manner must be based on traffic demands whether dynamic traffic or fluctuated traffic. Usage of multimedia devices also increased which in turn increased the demand for high throughput. Cochannel interference keep on changing or mitigations occur which can be handled by proper resource allocations. Network survival is by efficient usage of valid patis in the network by avoiding transmission failures and time slots’ effective usage. Originality/value Literature survey is carried out to find the methods which give better performance.

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Spherical Diffusion Model with Semi-Permeable Boundary: A Transfer Function Approach

Schäfer

Wicke

Haselmayr

et al. 2020

ICC 2020 - 2020 IEEE International Conference on Communications (ICC)

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The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications (e.g., assumption of an unbounded environment). In this paper, we develop a realistic model for particle diffusion in a bounded sphere and particle transport through a semi-permeable boundary. This model can be used for various applications, such as modeling of inter-/intra-cell communication or the release process of drug carriers. The proposed analytical model is based on a transfer function approach, which allows for fast numerical evaluation and provides insights into the impact of the relevant molecular communication system parameters. The proposed solution of the bounded spherical diffusion problem is formulated in terms of a state-space description and the semi-permeable boundary is accounted for by a feedback loop. Particle-based simulations verify the proposed modeling approach.

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Transfer function models for distributed-parameter systems with impedance boundary conditions

Cited by 9 publications

References 16 publications

Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

Analytical Models for Particle Diffusion and Flow in a Horizontal Cylinder with a Vertical Force

Cooperative optimization techniques in distributed MAC protocols – a survey

Spherical Diffusion Model with Semi-Permeable Boundary: A Transfer Function Approach

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