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Papers by Baran Can Aydın

Research paper thumbnail of Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

Research paper thumbnail of constant depth Focusing of long waves with finite crest over

Research paper thumbnail of New formulations for tsunami runup estimation

Research paper thumbnail of New Analytical Solution for Nonlinear Shallow Water-Wave Equations

Pure and Applied Geophysics, 2017

Research paper thumbnail of Wind set-down relaxation

Computer Modeling in Engineering and Sciences

We developed analytical solutions to the wind set-down and the wind set-down relaxation problems.... more We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear shallow-water wave equations are solved analytically as an initial-boundary value problem, with forced initial data derived from our wind set-down solution.

Research paper thumbnail of Mathematical Modelling of Doxycyline Release from Polycaprolactone Microspheres

Introduction The most popular biodegradable polymers for long-term delivery of hydrophilic drugs ... more Introduction The most popular biodegradable polymers for long-term delivery of hydrophilic drugs are polyesters as they show low degree of swelling in aqueous solutions. Among them PCL (poly-ε-caprolactone) is specifically found suitable for implantable or injectable delivery devices with slow biodegradation rate and non-acidic degradation environment. This polymer was approved by FDA for biomedical applications. Doxycycline (DOX) is a semi-synthetic antibiotic which elicits its antimicrobial activity by preventing the addition of amino acids to growing peptide chains in bacteria. DOX is one of the most stable tetracycline group members and has promised to be a good candidate for slow release formulations (Haerdi-Landerer, M.C. et al., 2008). In vitro DOX release studies have clearly indicated that use of DOX containing collagen-coated and uncoated PCL microparticles have potential for treatment for periodontitis (Aishwarya, S. et al., 2008). This study aimed to analyze the release ...

Research paper thumbnail of Tsunami focusing

Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography... more Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography caused by earthquakes, submarine/subaerial mass failures. They evolve substantially through three dimensional - 2 spatial+1 temporal - spreading as the initial surface deformation propagates. This is referred to as its directivity and focusing. A directivity function was first defined by Ben-Menahem (1961, Bull. Seismol. Soc. Am. 51, 401-435) using the source length and the rupture velocity. Okal (2003, Pure Appl. Geophys. 160, 2189-2221) discussed the details of the analysis of Ben-Menahem (1961) and demonstrated the distinct difference between the directivity patterns of landslide and earthquake generated tsunamis. Marchuk and Titov (1989, Proc. IUGG/IOC International Tsunami Symposium, July 31 - August 3, 1989, Novosibirsk, USSR. p.11-17) described the process of tsunami focusing for a rectangular initial deformation combining positive and negative surface displacements. They showed ...

Research paper thumbnail of Effect of Time-dependent Rupture on Tsunami Generation

Research paper thumbnail of Focusing of long waves with finite crest over sloping beach

Research paper thumbnail of Tsunami Amplification due to Focusing

Research paper thumbnail of Focusing of N-waves: A Possible Mechanism for Amplified Run-up

ABSTRACT The initial free-surface displacement generated by a submarine earthquake has a dipolar ... more ABSTRACT The initial free-surface displacement generated by a submarine earthquake has a dipolar nature, which is computed analytically by Okada's solution [1] and is finite crested. The resulting leading long wave has an N-wave shape as noted by Tadepalli & Synolakis [2, 3]. Here, we present a simple analytical solution of the linear shallow-water wave equations over a constant depth to study the propagation of a finite strip source. We show the existence of focusing points of dipolar initial displacements, i.e. points where wave amplification may be observed, due to the directional focusing of three waves, namely a positive wave from the center of elevation part and two positive waves from the sides of depression. N-wave focusing is not restricted to linear non-dispersive wave theory, but can also be observed using nonlinear shallow-water wave theory and dispersive theory. The location of the focusing point depends on the strip length. The focusing mechanism is an inherent property of the initial waveform and thus is not caused by bathymetric lenses, which can have a significant combined effect on the evolution of earthquake-generated tsunamis. Using the 1998 Papua New Guinea, 2006 Java and 2011 Japan tsunamis as examples, we discuss the geophysical implications of the focusing and how this can be related to abnormal high run-up values observed during these events, which were insufficiently explained so far. [1] Okada, Y. 1985 Surface deformation due to shear and tensile faults in a half-space. Bull. Seism. Soc. Am. 75, 1135-1154. [2] Tadepalli, S. & Synolakis, C. E. 1994 The run-up of N-waves on sloping beaches. Proc. R. Soc. Lond. A 445, 99-112. [3] Tadepalli, S. & Synolakis, C. E. 1996 Model for the leading waves of tsunamis. Phys. Rev. Lett. 77, 2141-2144.

Research paper thumbnail of Study on physiochemical structure and in vitro release behaviors of doxycycline-loaded PCL microspheres

Journal of Applied Polymer Science, 2014

Research paper thumbnail of Nonlinear analytical solution for landslide generated tsunamis

Gutenberg (1939 Bull. Seismol. Soc. Am. 29, 517-526.) reported that ``submarine landslides are to... more Gutenberg (1939 Bull. Seismol. Soc. Am. 29, 517-526.) reported that ``submarine landslides are to be considered at least as one of the chief causes, if not indeed the major cause of tsunamis.'' Recent tsunami events caused by landslides, including 1998 Papua New Guinea tsunami (Synolakis et al. 2002 Proc. R. Soc. A 458, 763-789), renewed interest for landslide generated tsunamis. We attempt to identify propagation and runup characteristics of subaerial and submarine landslides analytically. We solve the forced -nonhomogeneous- nonlinear shallow-water wave equations so that sliding volume is incorporated into the governing equations as a forcing term. We first transform the governing equations into a single linear partial differential equation applying the so-called hodograph transformation as in Kanoglu and Synolakis (2006 Phys. Rev. Lett. 97, 148501). However, unlike without forcing case, it is not possible to transform the governing nonlinear equations into a single line...

Research paper thumbnail of Assessing the source of the 2010 Chilean tsunami using DART data

There has been substantial interest in developing tsunami resilient communities for tsunami-prone... more There has been substantial interest in developing tsunami resilient communities for tsunami-prone regions worldwide following the Indian Ocean tsunami of 26 December 2004. In the United States, NOAA has accelerated its effort in developing a tsunami forecasting system. NOAA's forecasting methodology is based on the concept of a pre-computed tsunami scenario database which includes tsunami evolution from 100km x 50km earthquakes called tsunami source functions. These source functions have a slip value of 1m, and are placed along the subduction zones of the world oceans in several rows. Linearity of the tsunami propagation in the open ocean allows scaling and/or combination of the pre-computed propagation database source functions. The offshore scenario is obtained through scaling and/or combination of tsunami source functions constrained with Deep-ocean Assessment and Reporting of Tsunami (DART™) buoy measurements. Once the offshore scenario is constructed, this provides initial and boundary conditions for the high-resolution, site-specific, nonlinear local forecast products. The determination of the offshore scenario requires inversion of DART™ buoy measurements. We determine the event scenario using different minimization techniques, including least-square minimization and genetic algorithm search. Specifically, we tested different minimization functions, i.e., the sum of the squared residuals, the sum of the magnitudes of the residuals, the largest magnitude of the residuals, the sum of the squared residuals at the model peak and trough. In addition, we implemented earthquake magnitude for one of the minimization functions as a constraint. We used the 27 February 2010 Chile tsunami generated by a Mw 8.8 earthquake as a test case. In approximately three hours after its generation, the Chilean tsunami was first recorded at DART™ buoy 32412 then at the other DARTs in the region. We used one and/or several DART measurement(s) to test different minimization functions and constraints. We discuss minimization functions and constraints which might lead to better estimates at coastal tide gages using local forecast models.

Research paper thumbnail of Tsunami focusing

Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography... more Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography caused by earthquakes, submarine/subaerial mass failures. They evolve substantially through three dimensional - 2 spatial+1 temporal - spreading as the initial surface deformation propagates. This is referred to as its directivity and focusing. A directivity function was first defined by Ben-Menahem (1961, Bull. Seismol. Soc. Am.

Research paper thumbnail of Modeling of Tsunami Propagation and Inundation in the Aegean Sea

ABSTRACT Several tsunami forecasting systems have been developed based on pre-computed tsunami sc... more ABSTRACT Several tsunami forecasting systems have been developed based on pre-computed tsunami scenario databases with the aim to provide early warning to tsunami-prone regions worldwide. NOAA's tsunami forecasting system for the United States is such a system, based on the concept of a pre-computed tsunami scenario database consisting of 100km x 50km fault planes with a slip value of 1m, referred to as tsunami source functions. These source functions are placed along the subduction zones in several rows, covering known faults throughout the major ocean basins. Linearity of the tsunami propagation in the open ocean allows scaling and/or combination of the pre-computed tsunami source functions since propagation of tsunamis in deep sea is linear. In real time, a specific tsunami scenario can be obtained by inverting deep-ocean buoy measurements providing initial and boundary conditions for site-specific, high-resolution, nonlinear forecast models. The database can also be used to generate different scenario events to produce tsunami inundation maps for target shorelines. To date, tsunami source functions have not been computed along the subduction zones in Aegean Sea even though there are considerable number of tsunami events causing damages. Although one might argue that the possibility of such an event is rare, the coastlines are densely populated, developed, and hosts millions of tourists during the summer months. Therefore, even though the risk of an event might be small, the hazard is high. Considering the long shorelines and the general lack of public knowledge about preparedness, a tsunami event in the region would be disastrous. A database for historical tsunami events in the Aegean Sea has been compiled, providing potential source locations. This data has allowed us to create a tsunami propagation database for Aegean Sea. Once finalized, this pre-computed scenario database will be extremely useful in developing tsunami resilient communities in the region.

Research paper thumbnail of Focusing of long waves with finite crest over constant depth

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013

Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from th... more Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such asN-waves. We show the existence of focusing points forN-wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explai...

Research paper thumbnail of Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

Research paper thumbnail of constant depth Focusing of long waves with finite crest over

Research paper thumbnail of New formulations for tsunami runup estimation

Research paper thumbnail of New Analytical Solution for Nonlinear Shallow Water-Wave Equations

Pure and Applied Geophysics, 2017

Research paper thumbnail of Wind set-down relaxation

Computer Modeling in Engineering and Sciences

We developed analytical solutions to the wind set-down and the wind set-down relaxation problems.... more We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear shallow-water wave equations are solved analytically as an initial-boundary value problem, with forced initial data derived from our wind set-down solution.

Research paper thumbnail of Mathematical Modelling of Doxycyline Release from Polycaprolactone Microspheres

Introduction The most popular biodegradable polymers for long-term delivery of hydrophilic drugs ... more Introduction The most popular biodegradable polymers for long-term delivery of hydrophilic drugs are polyesters as they show low degree of swelling in aqueous solutions. Among them PCL (poly-ε-caprolactone) is specifically found suitable for implantable or injectable delivery devices with slow biodegradation rate and non-acidic degradation environment. This polymer was approved by FDA for biomedical applications. Doxycycline (DOX) is a semi-synthetic antibiotic which elicits its antimicrobial activity by preventing the addition of amino acids to growing peptide chains in bacteria. DOX is one of the most stable tetracycline group members and has promised to be a good candidate for slow release formulations (Haerdi-Landerer, M.C. et al., 2008). In vitro DOX release studies have clearly indicated that use of DOX containing collagen-coated and uncoated PCL microparticles have potential for treatment for periodontitis (Aishwarya, S. et al., 2008). This study aimed to analyze the release ...

Research paper thumbnail of Tsunami focusing

Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography... more Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography caused by earthquakes, submarine/subaerial mass failures. They evolve substantially through three dimensional - 2 spatial+1 temporal - spreading as the initial surface deformation propagates. This is referred to as its directivity and focusing. A directivity function was first defined by Ben-Menahem (1961, Bull. Seismol. Soc. Am. 51, 401-435) using the source length and the rupture velocity. Okal (2003, Pure Appl. Geophys. 160, 2189-2221) discussed the details of the analysis of Ben-Menahem (1961) and demonstrated the distinct difference between the directivity patterns of landslide and earthquake generated tsunamis. Marchuk and Titov (1989, Proc. IUGG/IOC International Tsunami Symposium, July 31 - August 3, 1989, Novosibirsk, USSR. p.11-17) described the process of tsunami focusing for a rectangular initial deformation combining positive and negative surface displacements. They showed ...

Research paper thumbnail of Effect of Time-dependent Rupture on Tsunami Generation

Research paper thumbnail of Focusing of long waves with finite crest over sloping beach

Research paper thumbnail of Tsunami Amplification due to Focusing

Research paper thumbnail of Focusing of N-waves: A Possible Mechanism for Amplified Run-up

ABSTRACT The initial free-surface displacement generated by a submarine earthquake has a dipolar ... more ABSTRACT The initial free-surface displacement generated by a submarine earthquake has a dipolar nature, which is computed analytically by Okada's solution [1] and is finite crested. The resulting leading long wave has an N-wave shape as noted by Tadepalli & Synolakis [2, 3]. Here, we present a simple analytical solution of the linear shallow-water wave equations over a constant depth to study the propagation of a finite strip source. We show the existence of focusing points of dipolar initial displacements, i.e. points where wave amplification may be observed, due to the directional focusing of three waves, namely a positive wave from the center of elevation part and two positive waves from the sides of depression. N-wave focusing is not restricted to linear non-dispersive wave theory, but can also be observed using nonlinear shallow-water wave theory and dispersive theory. The location of the focusing point depends on the strip length. The focusing mechanism is an inherent property of the initial waveform and thus is not caused by bathymetric lenses, which can have a significant combined effect on the evolution of earthquake-generated tsunamis. Using the 1998 Papua New Guinea, 2006 Java and 2011 Japan tsunamis as examples, we discuss the geophysical implications of the focusing and how this can be related to abnormal high run-up values observed during these events, which were insufficiently explained so far. [1] Okada, Y. 1985 Surface deformation due to shear and tensile faults in a half-space. Bull. Seism. Soc. Am. 75, 1135-1154. [2] Tadepalli, S. & Synolakis, C. E. 1994 The run-up of N-waves on sloping beaches. Proc. R. Soc. Lond. A 445, 99-112. [3] Tadepalli, S. & Synolakis, C. E. 1996 Model for the leading waves of tsunamis. Phys. Rev. Lett. 77, 2141-2144.

Research paper thumbnail of Study on physiochemical structure and in vitro release behaviors of doxycycline-loaded PCL microspheres

Journal of Applied Polymer Science, 2014

Research paper thumbnail of Nonlinear analytical solution for landslide generated tsunamis

Gutenberg (1939 Bull. Seismol. Soc. Am. 29, 517-526.) reported that ``submarine landslides are to... more Gutenberg (1939 Bull. Seismol. Soc. Am. 29, 517-526.) reported that ``submarine landslides are to be considered at least as one of the chief causes, if not indeed the major cause of tsunamis.'' Recent tsunami events caused by landslides, including 1998 Papua New Guinea tsunami (Synolakis et al. 2002 Proc. R. Soc. A 458, 763-789), renewed interest for landslide generated tsunamis. We attempt to identify propagation and runup characteristics of subaerial and submarine landslides analytically. We solve the forced -nonhomogeneous- nonlinear shallow-water wave equations so that sliding volume is incorporated into the governing equations as a forcing term. We first transform the governing equations into a single linear partial differential equation applying the so-called hodograph transformation as in Kanoglu and Synolakis (2006 Phys. Rev. Lett. 97, 148501). However, unlike without forcing case, it is not possible to transform the governing nonlinear equations into a single line...

Research paper thumbnail of Assessing the source of the 2010 Chilean tsunami using DART data

There has been substantial interest in developing tsunami resilient communities for tsunami-prone... more There has been substantial interest in developing tsunami resilient communities for tsunami-prone regions worldwide following the Indian Ocean tsunami of 26 December 2004. In the United States, NOAA has accelerated its effort in developing a tsunami forecasting system. NOAA's forecasting methodology is based on the concept of a pre-computed tsunami scenario database which includes tsunami evolution from 100km x 50km earthquakes called tsunami source functions. These source functions have a slip value of 1m, and are placed along the subduction zones of the world oceans in several rows. Linearity of the tsunami propagation in the open ocean allows scaling and/or combination of the pre-computed propagation database source functions. The offshore scenario is obtained through scaling and/or combination of tsunami source functions constrained with Deep-ocean Assessment and Reporting of Tsunami (DART™) buoy measurements. Once the offshore scenario is constructed, this provides initial and boundary conditions for the high-resolution, site-specific, nonlinear local forecast products. The determination of the offshore scenario requires inversion of DART™ buoy measurements. We determine the event scenario using different minimization techniques, including least-square minimization and genetic algorithm search. Specifically, we tested different minimization functions, i.e., the sum of the squared residuals, the sum of the magnitudes of the residuals, the largest magnitude of the residuals, the sum of the squared residuals at the model peak and trough. In addition, we implemented earthquake magnitude for one of the minimization functions as a constraint. We used the 27 February 2010 Chile tsunami generated by a Mw 8.8 earthquake as a test case. In approximately three hours after its generation, the Chilean tsunami was first recorded at DART™ buoy 32412 then at the other DARTs in the region. We used one and/or several DART measurement(s) to test different minimization functions and constraints. We discuss minimization functions and constraints which might lead to better estimates at coastal tide gages using local forecast models.

Research paper thumbnail of Tsunami focusing

Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography... more Tsunamis are long waves generated by impulsive disturbances of the seafloor or coastal topography caused by earthquakes, submarine/subaerial mass failures. They evolve substantially through three dimensional - 2 spatial+1 temporal - spreading as the initial surface deformation propagates. This is referred to as its directivity and focusing. A directivity function was first defined by Ben-Menahem (1961, Bull. Seismol. Soc. Am.

Research paper thumbnail of Modeling of Tsunami Propagation and Inundation in the Aegean Sea

ABSTRACT Several tsunami forecasting systems have been developed based on pre-computed tsunami sc... more ABSTRACT Several tsunami forecasting systems have been developed based on pre-computed tsunami scenario databases with the aim to provide early warning to tsunami-prone regions worldwide. NOAA's tsunami forecasting system for the United States is such a system, based on the concept of a pre-computed tsunami scenario database consisting of 100km x 50km fault planes with a slip value of 1m, referred to as tsunami source functions. These source functions are placed along the subduction zones in several rows, covering known faults throughout the major ocean basins. Linearity of the tsunami propagation in the open ocean allows scaling and/or combination of the pre-computed tsunami source functions since propagation of tsunamis in deep sea is linear. In real time, a specific tsunami scenario can be obtained by inverting deep-ocean buoy measurements providing initial and boundary conditions for site-specific, high-resolution, nonlinear forecast models. The database can also be used to generate different scenario events to produce tsunami inundation maps for target shorelines. To date, tsunami source functions have not been computed along the subduction zones in Aegean Sea even though there are considerable number of tsunami events causing damages. Although one might argue that the possibility of such an event is rare, the coastlines are densely populated, developed, and hosts millions of tourists during the summer months. Therefore, even though the risk of an event might be small, the hazard is high. Considering the long shorelines and the general lack of public knowledge about preparedness, a tsunami event in the region would be disastrous. A database for historical tsunami events in the Aegean Sea has been compiled, providing potential source locations. This data has allowed us to create a tsunami propagation database for Aegean Sea. Once finalized, this pre-computed scenario database will be extremely useful in developing tsunami resilient communities in the region.

Research paper thumbnail of Focusing of long waves with finite crest over constant depth

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013

Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from th... more Tsunamis are long waves that evolve substantially, through spatial and temporal spreading from their source region. Here, we introduce a new analytical solution to study the propagation of a finite strip source over constant depth using linear shallow-water wave theory. This solution is not only exact, but also general and allows the use of realistic initial waveforms such asN-waves. We show the existence of focusing points forN-wave-type initial displacements, i.e. points where unexpectedly large wave heights may be observed. We explain the effect of focusing from a strip source analytically, and explore it numerically. We observe focusing points using linear non-dispersive and linear dispersive theories, analytically; and nonlinear non-dispersive and weakly nonlinear weakly dispersive theories, numerically. We discuss geophysical implications of our solutions using the 17 July 1998 Papua New Guinea and the 17 July 2006 Java tsunamis as examples. Our results may also help to explai...