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Kozlov, Vladimir
Alternative names
Publications (10 of 90) Show all publications
Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2018). A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients.
Open this publication in new window or tab >>A Modification to the Kirchhoff Conditions at a Bifurcation and Loss Coefficients
2018 (English)Report (Other academic)
Abstract [en]

One dimensional models for fluid flow in tubes are frequently used tomodel complex systems, such as the arterial tree where a large numberof vessels are linked together at bifurcations. At the junctions transmission conditions are needed. One popular option is the classic Kirchhoffconditions which means conservation of mass at the bifurcation andprescribes a continuous pressure at the joint.

In reality the boundary layer phenomena predicts fast local changesto both velocity and pressure inside the bifurcation. Thus it is not appropriate for a one dimensional model to assume a continuous pressure. In this work we present a modification to the classic Kirchhoff condi-tions, with a symmetric pressure drop matrix, that is more suitable forone dimensional flow models. An asymptotic analysis, that has beencarried out previously shows that the new transmission conditions hasen exponentially small error.

The modified transmission conditions take the geometry of the bifurcation into account and can treat two outlets differently. The conditions can also be written in a form that is suitable for implementationin a finite difference solver. Also, by appropriate choice of the pressuredrop matrix we show that the new transmission conditions can producehead loss coefficients similar to experimentally obtained ones.

Publisher
p. 11
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:5
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-147718 (URN)LiTH-MAT-R--2018/05--SE (ISRN)
Available from: 2018-05-07 Created: 2018-05-07 Last updated: 2018-05-07Bibliographically approved
Ghosh, A., Kozlov, V., Nazarov, S. A. & Rule, D. (2018). A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe.
Open this publication in new window or tab >>A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe
2018 (English)Report (Other academic)
Abstract [en]

We present a two dimensional model describing the elastic behaviour of the wall of a curved pipe to model blood vessels in particular. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with the surrounding material and the fluid flowing inside into account and is obtained via a dimension reduction procedure. The curvature and twist of the vessel axis as well as the anisotropy of the laminate wallpresent the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of vessels and their walls are supplied with explicit systems of dierential equations at the end.

Publisher
p. 20
Series
LiTH-MAT-R, ISSN 0348-2960 ; 6
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-148014 (URN)LiTH-MAT-R--2018/06--SE (ISRN)
Available from: 2018-05-24 Created: 2018-05-24 Last updated: 2018-05-24Bibliographically approved
Kozlov, V., Nazarov, S. A. & Zavorokhin, G. (2018). Pressure drop matrix for a bifuration of an artery with defects. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Pressure drop matrix for a bifuration of an artery with defects
2018 (English)Report (Other academic)
Abstract [en]

We consider a bifurcation of an artery. The influence of defects of the vessel's wall near the bifurcation point on the pressure drop matrix is analyzed. The elements of this matrix are included in the modified Kirchhoff transmission conditions, which were introduced earlier in [1], [2], and which describe adequately the total pressure loss at the bifurcation point of the flow passed through it.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2018. p. 22
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2018:7
Keywords
Stokes' flow, bifurcation of a blood vessel, modified Kirchhoff conditions, pressure drop matrix, total pressure loss
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-148597 (URN)LiTH-MAT-R--2018/07--SE (ISRN)
Available from: 2018-06-14 Created: 2018-06-14 Last updated: 2018-06-15Bibliographically approved
Berntsson, F., Karlsson, M., Kozlov, V. & Nazarov, S. A. (2016). A one-dimensional model of viscous blood flow in an elastic vessel. Applied Mathematics and Computation, 274, 125-132
Open this publication in new window or tab >>A one-dimensional model of viscous blood flow in an elastic vessel
2016 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 274, p. 125-132Article in journal (Refereed) Published
Abstract [en]

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessels wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE INC, 2016
Keywords
Blood flow; Linear model; Asymptotic analysis; Dimension reduction; Numerical simulation
National Category
Mathematics Mechanical Engineering
Identifiers
urn:nbn:se:liu:diva-124453 (URN)10.1016/j.amc.2015.10.077 (DOI)000367521900013 ()
Available from: 2016-02-02 Created: 2016-02-01 Last updated: 2017-11-30
Kozlov, V. A. & Nazarov, S. A. (2016). A simple one-dimensional model of a false aneurysm in the femoral artery. Journal of Mathematical Sciences, 214(3), 287-301
Open this publication in new window or tab >>A simple one-dimensional model of a false aneurysm in the femoral artery
2016 (English)In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 214, no 3, p. 287-301Article in journal (Refereed) Published
Abstract [en]

Using the dimension reduction procedure, a one-dimensional model of a periodic blood flow in the artery through a small hole in a thin elastic wall to a spindle-shaped hematoma, is constructed. This model is described by a system of two parabolic and one hyperbolic equations provided with mixed boundary and periodicity conditions. The blood exchange between the artery and the hematoma is expressed by the Kirchhoff transmission conditions. Despite the simplicity, the constructed model allows us to describe the damping of a pulsating blood flow by the hematoma and to determine the condition of its growth. In medicine, the biological object considered is called a false aneurysm.

Place, publisher, year, edition, pages
Springer, 2016
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-127727 (URN)10.1007/s10958-016-2778-1 (DOI)
Available from: 2016-05-11 Created: 2016-05-11 Last updated: 2017-11-30Bibliographically approved
Kozlov, V. & Thim, J. (2016). Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators. Journal of Spectral Theory, 6(1), 99-135
Open this publication in new window or tab >>Hadamard type asymptotics for eigenvalues of the Neumann problem for elliptic operators
2016 (English)In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403, Vol. 6, no 1, p. 99-135Article in journal (Refereed) Published
Abstract [en]

This paper considers how the eigenvalues of the Neumann problem for an elliptic operator depend on the domain. The proximity of two domains is measured in terms of the norm of the difference between the two resolvents corresponding to the reference domain and the perturbed domain, and the size of eigenfunctions outside the intersection of the two domains. This construction enables the possibility of comparing both nonsmooth domains and domains with different topology. An abstract framework is presented, where the main result is an asymptotic formula where the remainder is expressed in terms of the proximity quantity described above when this is relatively small. As an application, we develop a theory for the Laplacian in Lipschitz domains. In particular, if the domains are assumed to be C-1,C-alpha regular, an asymptotic result for the eigenvalues is given together with estimates for the remainder, and we also provide an example which demonstrates the sharpness of our obtained result.

Place, publisher, year, edition, pages
EUROPEAN MATHEMATICAL SOC, 2016
Keywords
Hadamard formula; domain variation; asymptotics of eigenvalues; Neumann problem
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-129508 (URN)10.4171/JST/120 (DOI)000376418300005 ()
Available from: 2016-06-20 Created: 2016-06-20 Last updated: 2017-11-28
Kozlov, V., Vakulenko, S. & Wennergren, U. (2016). Hamiltonian dynamics for complex food webs. PHYSICAL REVIEW E, 93(3), 032413
Open this publication in new window or tab >>Hamiltonian dynamics for complex food webs
2016 (English)In: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 93, no 3, p. 032413-Article in journal (Refereed) Published
Abstract [en]

We investigate stability and dynamics of large ecological networks by introducing classical methods of dynamical system theory from physics, including Hamiltonian and averaging methods. Our analysis exploits the topological structure of the network, namely the existence of strongly connected nodes (hubs) in the networks. We reveal new relations between topology, interaction structure, and network dynamics. We describe mechanisms of catastrophic phenomena leading to sharp changes of dynamics and hence completely altering the ecosystem. We also show how these phenomena depend on the structure of interaction between species. We can conclude that a Hamiltonian structure of biological interactions leads to stability and large biodiversity.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2016
National Category
Mathematics Biological Sciences
Identifiers
urn:nbn:se:liu:diva-127435 (URN)10.1103/PhysRevE.93.032413 (DOI)000372724300008 ()27078396 (PubMedID)
Note

Funding Agencies|Linkoping University, Government of Russian Federation [074-U01]; Russian Fund of Basic Research [16-01-00648]; US National Institutes of Health [RO1 OD010936]

Available from: 2016-05-01 Created: 2016-04-26 Last updated: 2016-05-17
Kozlov, V. & Nazarov, A. (2016). Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge. Journal of Mathematical Analysis and Applications, 435(1), 210-228
Open this publication in new window or tab >>Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 435, no 1, p. 210-228Article in journal (Refereed) Published
Abstract [en]

We consider an oblique derivative problem in a wedge for non-divergence parabolic equations with time-discontinuous coefficients. We obtain weighted coercive estimates of solutions in anisotropic Sobolev spaces. (C) 2015 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016
Keywords
Parabolic equations in a wedge; Discontinuous coefficients; Weighted coercive estimates; Anisotropic Sobolev spaces
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-124076 (URN)10.1016/j.jmaa.2015.10.029 (DOI)000365928200011 ()
Available from: 2016-01-25 Created: 2016-01-19 Last updated: 2017-11-30
Kozlov, V. & Rossmann, J. (2016). On the nonstationary Stokes system in a cone. Journal of Differential Equations, 260(12), 8277-8315
Open this publication in new window or tab >>On the nonstationary Stokes system in a cone
2016 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 260, no 12, p. 8277-8315Article in journal (Refereed) Published
Abstract [en]

The authors consider the Dirichlet problem for the nonstationary Stokes system in a threedimensional cone. They obtain existence and uniqueness results for solutions in weighted Sobolev spaces and prove a regularity assertion for the solutions. (C) 2016 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016
Keywords
Nonstationary Stokes system; Conical points
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-128716 (URN)10.1016/j.jde.2016.02.024 (DOI)000375234300001 ()
Available from: 2016-06-07 Created: 2016-05-30 Last updated: 2017-11-30
Kozlov, V., Radosavljevic, S., Tkachev, V. & Wennergren, U. (2016). Persistence analysis of the age-structured population model on several patches. In: J. Vigo-Aguiar (Ed.), Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III: . Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016 (pp. 717-727). Paper presented at Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016. Universidad de Cádiz, 3
Open this publication in new window or tab >>Persistence analysis of the age-structured population model on several patches
2016 (English)In: Proceedings of the 16th International Conference on Mathematical Methods in Science and Engineering, July 4-8, Rota, Cadiz, Spain, Vol. III / [ed] J. Vigo-Aguiar, Universidad de Cádiz , 2016, Vol. 3, p. 717-727Chapter in book (Refereed)
Abstract [en]

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the system in time-independent case and for periodically changing environment. Under the assumption that every patch can be reached from every other patch, directly or through several intermediary patches, and that net reproductive operator has spectral radius larger than one, we prove that population is persistent on all patches. If the spectral radius is less or equal one, extinction on all patches is imminent.

Place, publisher, year, edition, pages
Universidad de Cádiz, 2016
Keywords
age-structure, persistence, Kermack-McKendrick equation, Lotcka-Volterra equation
National Category
Biological Sciences Mathematics
Identifiers
urn:nbn:se:liu:diva-130231 (URN)9788460860822 (ISBN)
Conference
Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2016
Note

Associate Editors

P. Schwerdtfeger (New Zealand), W. Sprößig (Germany), N. Stollenwerk (Portugal), Pino Caballero (Spain), J. Cioslowski (Poland), J. Medina (Spain), I. P. Hamilton (Canada), J. A. Alvarez-Bermejo (Spain)

Available from: 2016-07-21 Created: 2016-07-21 Last updated: 2016-08-31Bibliographically approved
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