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1
Content available Calculating the second-order hydrodynamic force on fixed and floating tandem cylinders
Motallebi Mohammad, Ghafari Hamidreza, Ghassemi Hassan, Shokouhian Mehdi
Zeszyty Naukowe Akademii Morskiej w Szczecinie
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2020
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nr 62 (134)
108--115
EN
In this paper, the second-order hydrodynamic force on fixed and floating tandem cylinders has been calculated and different parameters have been taken into consideration. An incident wave is diffracted by the fixed cylinder, and as a result low-frequency waves radiate toward the floating cylinder and cause low-frequency second-order hydrodynamic forces to act on the surface of the floating cylinder. The interactions between the fixed and floating cylinders have been investigated by changing the distance between them, as well as the draft and radius of the floating cylinder. By employing perturbation series analysis over the wetted surface, the second-order wave excitation force has been calculated. The maximum force applied on the floating cylinder becomes non-dimensional when considering it with and without the fixed cylinder. The results showed the effect that the existence of the fixed cylinder had on the increase in the second-order forces is quite evident where, for a significant parameter of the floating cylinder, the force in the heave direction was enhanced by up to 1.55 times.
2
Content available Eigenvalue asymptotics for potential type operators on lipschitz surfaces of codimension greater than 1
Rozenblum G., Tashchiyan G.
Opuscula Mathematica
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2018
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Vol. 38, no. 5
733--758
EN
For potential type integral operators on a Lipschitz submanifold the asymptotic formula for eigenvalues is proved. The reasoning is based upon the study of the rate of operator convergence as smooth surfaces approximate the Lipschitz one.
3
Content available remote The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn
Kohr M.
Archives of Mechanics
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2007
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Vol. 59, nr 3
283-304
EN
The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0
4
Content available Application of potential theory in calculating wave-induced vertical forces on horizontal cylinders near a plane boundary
Marcinkowski T., Wilde P.
Archives of Hydro-Engineering and Environmental Mechanics
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2006
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Vol. 53, nr 1
49-69
EN
Hydrodynamic forces acting on a horizontal cylinder located in the vicinity of the bottom are analyzed by a diffraction theory which solves the problem in terms of a velocity potential. The cylinder is assumed to be rigidly anchored to the bottom at a sufficient depth, so that it has no influence on the surface profile. The potential function φ is defined as the sum of the incident wave velocity potential φ w and the scattered wave velocity potential φa. The results of measurements of wave-induced pressures and forces on a horizontal cylinder located close to the bottom are compared with the theoretical solution based on the potential theory for incompressible, perfect fluid and ideal boundary conditions at the bottom and the surface of the cylinder. The experiments were carried out in the Large Wave Channel in Hannover with a cylinder of 0.8 m diameter. Thus the results are in a scale which corresponds to real pipelines. The analysis shows that the potential theory explains the components with double frequency of the wave in pressures and vertical forces as far as the amplitudes are concerned. In the experiments, the Keulegan-Carpenter number is rather low and the inertia hydrodynamic forces on the cylinder are dominant. It seems that the observed phase shift between the force component and the wave results from the energy dissipation which is not considered in the theoretical solution.
5
Content available remote One-dimensional symmetric stable Feynman-Kac semigroups
Byczkowska H., Byczkowski T.
Probability and Mathematical Statistics
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2001
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Vol. 21, Fasc. 2
381--404
EN
We investigate here one-dimensional Feynman-Kac semigroups based on symmetric α-stable processes. We begin with establishing the properties of Green operators of intervals and halflines on functions from the Kato class. Then we provide a sufficient condition for gaugeability of the halfline(−∞, b) and evaluate the critical value β.
6
Content available remote Martin representation for α-harmonic functions
Michalik K., Samotij K.
Probability and Mathematical Statistics
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2000
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Vol. 20, Fasc. 1
75--91
EN
Let D be a nonempty open bounded subset of Rd, d ≥2, and let 0 < α < 2. For α-harmonic functions on D vanishing outside D an analogue of the Martin representation for harmonic functions is derived.
7
Content available remote Hoelder continuity property of composite Julia sets
Kosek M.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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Vol. 46, no 4
391-399
EN
In this paper we consider the composite Julia associated with a finite family of the proper polynomial mappings in [C^n]. We show its pluricomplex Green function is Hoelder continous. This yields in particular that the set preserves Markov's inequality.
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