https://www.fmcostanzo.com/current-class-schedule daily 0.75 2017-07-24 https://www.fmcostanzo.com/video-gallery daily 0.75 2017-08-01 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/5980bd043e00be810c3d3922/1501087466709/ Research Videos - Mesh details the simulation in https://youtu.be/qt1DeCFZECQ. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c5d6e58c62b0e4bc9f34/1501087466709/ Research Videos - Mesh details the simulation in https://youtu.be/qt1DeCFZECQ. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c6df5fd63bfe16dc4f3e/1501087190883/ Research Videos https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c6f6f7e0ab751a292701/1501087496027/ Research Videos - Mesh details the simulation in https://youtu.be/qt1DeCFZECQ. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c717d2b8576d2caf11c6/1501087515044/ Research Videos - Floating Ball https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c72d440243f85af4fe53/1501087554566/ Research Videos - Hydrocephalic brain swelling https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c74c29687fd19068a6a3/1501087576406/ Research Videos - YouTube https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c76f4c0dbf1b6306993f/1501087599551/ Research Videos - YouTube https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c77ea803bbc3289bb352/1501087614832/ Research Videos - YouTube https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c794914e6be6b3890610/1501087638168/ Research Videos https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c794b3db2b5151e2fe71/1501087643349/ Research Videos - Acoustofluidic coating of particles and cells https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7949de4bb3a6c54d447/1501609220485/ Research Videos - Acoustofluidic coating of particles and cells https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c79ebf629a80c56bc46a/1501605750737/ Research Videos - Sub-micrometer-precision, three-dimensional (3D) hydrodynamic focusing... https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c79ed482e958fc171033/1501605750706/ Research Videos - Sub-micrometer-precision, three-dimensional (3D) hydrodynamic focusing... https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7a803596e3ee469a5b4/1501605750734/ Research Videos - A reliable, programmable acoustofluidic pump powered by oscillating sharp-edge structures https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7a8c534a518fc6e0191/1501605750739/ Research Videos - A reliable, programmable acoustofluidic pump powered by oscillating sharp-edge structures https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7b4db29d664b6072fa2/1501605750792/ Research Videos - An acoustofluidic micromixer based on oscillating sidewall sharp-edges https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7c2e45a7c547a9dcff7/1501605750797/ Research Videos - An acoustofluidic sputum liquefier https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5978c5c73e00be7250d7d390/5978c7cc2994ca3b035dc2e4/1501605750846/ Research Videos - Standing surface acoustic wave (SSAW)-based microfluidic cytometer https://www.fmcostanzo.com/home-1 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef14aa1072eb9ee15/1503532884344/KeyAchievements3-1.jpg Home - Fig. 1 Configuration of 3D benchmark. The results of the simulation consists in tracking the displacement of the point A(t) in the figure and in determining the hydrodynamic forces acting on rigid obstacle and flexible bar system. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef7e0abbcaa713df9/1503532901425/KeyAchievements3-2.jpg Home - Fig. 2 Vertical channel containing viscous fluid through which a small incompressible disk is descending: (a) system’s geometry; (b) initial conditions (disk released from rest in a quiescent fluid); (c) detail of mesh of the immersed body. The disk’s terminal velocity is denoted by Ut. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccee9bfdfdf306062a3/1503532919124/KeyAchievements3-3.jpg Home - Fig. 3 Frame from animation showing the motion of a flexible flag as described in the FSI 2 benchmark by Hron and Turek. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/5989b5204c0dbf9c31494a02/1502197025343/KeyAchievements3-1.jpg Home https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0deb8a79ba9c19175a7/1503518260035/ResearchInterest-3.jpg Home - Fig. 3 Numerical prediction of the motion of a flexible tail flapping as fluids moves around it. This calculation is, which is part of a well-known benchmarking computational suite, was made to show that a new approach to solve fluid-structure interaction problems was indeed accurate and effective. Fluid-structure interaction is the study of the deformation of structures when they interact with a fluid in contact with them. The human body is a "gold-mine" of such problems. Here are just a few examples: blood flowing though flexible vasculature, food moving through the stomach and the intestine, brain pulsating while surrounded by cerebrospinal fluid. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0db59cc68c69d2fa19b/1503518246898/ResearchInterest-2.jpg Home - Fig. 2 Numerically predicted particle trajectories in a microacoustofluidic device in response to a high-frequency excitation of the substrate using surface acoustic waves. This calculation is part of a study to provide accurate engineering tools to design the next generation of diagnostic devices in biomedical applications. The devices are part of a growing technological trend called "lab-on-a-chip" (). This technology promises the ability to carry out in the palm of a hand a host of biochemical tests that nowadays require a well-equipped laboratory. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0d6cd39c3b6a6035948/1503518191785/ResearchInterest-1.jpg Home - Fig 1 Numerical prediction of the radial component of the velocity of interstitial fluid relative to that of the tissue in response to the peristaltic motion of the wall of a typical penetrating artery in brain. This calculation is part of a study addressing an important open question in brain physiology: how are toxic metabolites cleared from brain tissue? When these metabolites accumulate in brain tissue various pathologies arise, including Alzheimer's disease. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847441d482e94a17e8030c/59847460db29d66f894946f7/1503606790880/francesco-profile-image.jpg Home Francesco Costanzo, Ph.D. Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaadf9a61e30f52e566f/1503532853996/KeyAchievements2-3w.jpg Home - Fig. 3 Ezb Formulation: magnitude of the (a) Lagrangian velocity and (b) Eulerian velocity for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The Ezbc formulation (results in this figure) yields results that we believe are erroneous. The lines represent the streamlines of the respective velocities. Here the Lagrangian velocity streamlines cross the channel walls, indicating an unphysical mass flow across the channel walls. By contrast, consistent with the boundary conditions imposed in Ezbc formulation, here the Eulerian velocity streamlines do not cross the channel. These results are not supported by experimental evidence reported in Barnkob et al. (2016). https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaaa579fb34211773af1/1503532835124/KeyAchievements2-2.jpg Home - Fig. 2 ALE Formulation: magnitude of the Lagrangian-mean velocity (a) and of the Eulerian velocity (b) for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The lines represent the streamlines of the respective velocities. The Lagrangian velocity streamlines do not cross the channel walls, indicating no mass flow across the channel walls, while the Eulerian velocity streamlines cross the channel walls as though there were an outflow across the channel walls. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaa69f8dce3deaf8f48b/1503532806408/KeyAchievements2-1.jpg Home - Fig. 1 Microfluidic channel in a soft polymer actuated by surface acoustic waves. The surface acoustic waves leak energy into the polymer and microchannel and as a consequence, a pseudo-standing wave field arises. This field leads to acoustic streaming drag forces and radiation forces on suspended microparticles. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/5989b3bc914e6b1524ba5891/1502196673687/KeyAchievements2-1.jpg Home https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3bf43b552f89f5643c/1503517080767/KeyAchievements1-3.png Home - Method of Manufactured Solutions - 3 Convergence rates for the L2-norm of the error at t = 0.02s for a dynamic evolution without stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a59cc68d05673d40b/1503517056508/KeyAchievements1-2.jpg Home - Method of Manufactured Solutions - 2 Magnitude of fluid velocity in a dynamic evolution without stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a8fd4d2fa52d38a11/1503517043353/KeyAchievements1-1.jpg Home - Method of Manufactured Solutions - 1 Magnitude of fluid velocity in a static evolution with stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/5989b2c5579fb3fb9606878d/1502196422968/KeyAchievements1-1.jpg Home https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59846dfff9a61e76c6ee7cfa/59846e4c1e5b6c1be8a73169/1503428996481/texas-a-and-m.jpg Home Texas A&M University https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59846dfff9a61e76c6ee7cfa/59846e128419c27e055effde/1503429029545/politecnico-milano.jpg Home https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/5980ffdff14aa116f2d686ab/1503516600266/msc-evening-image.jpg Home https://www.fmcostanzo.com/honors-awards-1 daily 0.75 2017-08-07 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Honors Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810116d482e9a091b508a2/1501626647725/msc-evening-image.jpg Honors https://www.fmcostanzo.com/research daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8b8d2b85710609ab17d/1503586590807/KeyAchievements6-3.jpg Research - Fig. 3 Comparison between the nondimensional shear (μ) and effective shear (μeff ) moduli for the Gent Model with λz = 1, I m = 500 and c2 /c1 = 1 , 1, 2. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8b4ccc5c5e6c8ab6138/1503586567684/KeyAchievements6-2.jpg Research - Fig. 2 Comparison between the nondimensional shear (μ) and effective shear (μeff) moduli for the Fung model for various values of λz and a = 0.5. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8ac4c0dbf3e6afa27d0/1503586541111/KeyAchievements6-1.jpg Research - Fig. 1 Idealized geometry of a vessel like the esophagus or an artery. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/5989ba68e45a7cfe22b1b8b1/1502198378345/KeyAchievements6-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb7a7131a589ecf50e4a/1503587285305/KeyAchievements7-3.jpg Research - Fig. 3 - Velocity Evolution A ball released in a fluid container and floating to the top: velocity evolution. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb78f43b556c0c88ae12/1503587261745/KeyAchievements7-2.jpg Research - Fig. 2 - Pressure Evolution A ball released in a fluid container and floating to the top: pressure evolution. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb75f9a61e79d14e55b1/1503587239221/KeyAchievements7-1.jpg Research - Fig. 1 - Key Result Key result of the paper: The discrete formulation has the same formal energy estimate as the abstract formulation. This result implies that the discrete formulation is stable.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fe3e45a7c310e02286d/1503535168598/KeyAchievements5-3.jpg Research - Fig. 3 Plots of the velocity vbead in Eqn (20) corresponding to the boundary conditions in (a) eqn (14) and (b) eqn (15). The color map represents the magnitude of vbead whereas the lines are some of the streamlines of the vbead field. The channel dimensions are L = 300 μm (horizontal dimension), H = 600 μm (vertical dimension), α = 15° (sharp edge angle), and h = 200 μm (height of the sharp edge). The wall displacement was only in the vertical direction with magnitude 1 μm. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fde37c581435a2ab1b6/1503535149182/KeyAchievements5-2.jpg Research - Fig. 2 Experimentally observed trajectories of 1.9 μm diameter fluorescent polystyrene beads in our acoustically oscillated micro-mixer with sharp edges. The geometry of the microchannel is described in Fig. 1(c) except for the fact that here, the tips of the sharp edges are 200 μm from the wall instead of 250 μm. The driven oscilla- tion is harmonic with a frequency equal to 4.75 kHz. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fd7be42d6df90339fa6/1503535126599/KeyAchievements5-1.jpg Research - Fig. 1 (a) Schematic of the device showing a microfluidic channel with sharp-edge structures on its side walls. The channel walls are subjected to a time-harmonic excitation produced by a piezoelectric transducer placed on one side of the channel. (b) Typical micro streaming patterns produced in the fluid occupying the channel as a response to piezoelectric excitation. (c) Typical geometric dimensions of the corrugated channel. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/5989b76ce45a7cfe22b1905c/1502197613253/KeyAchievements5-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bf4f5e231b03da5fc66/1503603705708/actuation_movie_crop.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bdfccc5c51d364466c5/1503603682762/ok_tracks_20_um.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bd5be42d6c9ac3f43e4/1503603672664/ok_tracks_10_um.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bcdbe42d6c9ac3f430d/1503603664213/ok_tracks_08_um.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bbee58c624231843d67/1503603653546/ok_tracks_04_um.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f27f0be6594169d420cd3/1503603631251/ok_tracks_01_um.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2794ff7c5069b54ce453/1503602655311/p1_movie.gif Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/5989b63ef14aa1c7d2b8cd7c/1502197311668/KeyAchievements4-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef14aa1072eb9ee15/1503532884344/KeyAchievements3-1.jpg Research - Fig. 1 Configuration of 3D benchmark. The results of the simulation consists in tracking the displacement of the point A(t) in the figure and in determining the hydrodynamic forces acting on rigid obstacle and flexible bar system. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef7e0abbcaa713df9/1503532901425/KeyAchievements3-2.jpg Research - Fig. 2 Vertical channel containing viscous fluid through which a small incompressible disk is descending: (a) system’s geometry; (b) initial conditions (disk released from rest in a quiescent fluid); (c) detail of mesh of the immersed body. The disk’s terminal velocity is denoted by Ut. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccee9bfdfdf306062a3/1503532919124/KeyAchievements3-3.jpg Research - Fig. 3 Frame from animation showing the motion of a flexible flag as described in the FSI 2 benchmark by Hron and Turek. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/5989b5204c0dbf9c31494a02/1502197025343/KeyAchievements3-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Research Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaadf9a61e30f52e566f/1503532853996/KeyAchievements2-3w.jpg Research - Fig. 3 Ezb Formulation: magnitude of the (a) Lagrangian velocity and (b) Eulerian velocity for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The Ezbc formulation (results in this figure) yields results that we believe are erroneous. The lines represent the streamlines of the respective velocities. Here the Lagrangian velocity streamlines cross the channel walls, indicating an unphysical mass flow across the channel walls. By contrast, consistent with the boundary conditions imposed in Ezbc formulation, here the Eulerian velocity streamlines do not cross the channel. These results are not supported by experimental evidence reported in Barnkob et al. (2016). https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaaa579fb34211773af1/1503532835124/KeyAchievements2-2.jpg Research - Fig. 2 ALE Formulation: magnitude of the Lagrangian-mean velocity (a) and of the Eulerian velocity (b) for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The lines represent the streamlines of the respective velocities. The Lagrangian velocity streamlines do not cross the channel walls, indicating no mass flow across the channel walls, while the Eulerian velocity streamlines cross the channel walls as though there were an outflow across the channel walls. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaa69f8dce3deaf8f48b/1503532806408/KeyAchievements2-1.jpg Research - Fig. 1 Microfluidic channel in a soft polymer actuated by surface acoustic waves. The surface acoustic waves leak energy into the polymer and microchannel and as a consequence, a pseudo-standing wave field arises. This field leads to acoustic streaming drag forces and radiation forces on suspended microparticles. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/5989b3bc914e6b1524ba5891/1502196673687/KeyAchievements2-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3bf43b552f89f5643c/1503517080767/KeyAchievements1-3.png Research - Method of Manufactured Solutions - 3 Convergence rates for the L2-norm of the error at t = 0.02s for a dynamic evolution without stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a59cc68d05673d40b/1503517056508/KeyAchievements1-2.jpg Research - Method of Manufactured Solutions - 2 Magnitude of fluid velocity in a dynamic evolution without stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a8fd4d2fa52d38a11/1503517043353/KeyAchievements1-1.jpg Research - Method of Manufactured Solutions - 1 Magnitude of fluid velocity in a static evolution with stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/5989b2c5579fb3fb9606878d/1502196422968/KeyAchievements1-1.jpg Research https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/5980da7cd2b857167c444b59/1501616775202/msc-evening-image.jpg Research https://www.fmcostanzo.com/teaching daily 0.75 2017-08-07 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3f914e6bb95b91199a/1503607134274/statics.jpg Teaching https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3fbe65942a56757f92/1503607239146/statics-and-dynamics.jpg Teaching https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3e15d5db25d976f80a/1503607231387/dynamics.jpg Teaching https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Teaching Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/5980eac4e58c626887dd0a92/1501620939729/msc-evening-image.jpg Teaching https://www.fmcostanzo.com/publications-1 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f203e3e00be6dec58937d/1503600733188/ResearchEyeCandy-2.jpg Books & Parts of Books Acoustofluidic micromixer from N. Nama, P.-H. Huang, T. J. Huang, and F. Costanzo, ``Investigation of micromixing by acoustically oscillated sharp-edges,'' Biomicrofluidics, 10 (2016), pp. 024124–1–024124–17. DOI: 10.1063/1.4946875; PMID: 27158292; PMCID: PMC4833753. The details of the theoretical framework are in N. Nama, P.-H. Huang, T. J. Huang, and F. Costanzo, "Investigation of acoustic streaming patterns around oscillating sharp edges," Lab on a Chip, 14 (2014), pp. 2824–2836. DOI: 10.1039/c4lc00191e; PMID: 24903475; PMCID: PMC4096312. A much improved analytical and numerical framework is in N. Nama, T. J. Huang, and F. Costanzo, "Acoustic streaming: A Lagrangian–Eulerian perspective," Journal of Fluid Mechanics, 825 (2017), pp. 600–630. DOI: 10.1017/jfm.2017.338.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Books & Parts of Books Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3f914e6bb95b91199a/1503607134274/statics.jpg Books & Parts of Books https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3fbe65942a56757f92/1503607239146/statics-and-dynamics.jpg Books & Parts of Books https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3e15d5db25d976f80a/1503607231387/dynamics.jpg Books & Parts of Books https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810563ebbd1a87ef37ab2a/1501627749080/msc-evening-image.jpg Books & Parts of Books https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810588bebafbf5a6801336/1501627785969/msc-evening-image.jpg Books & Parts of Books https://www.fmcostanzo.com/refereed-papers-1 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Publications Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f1fb015d5dbb47b3dd025/1503600980178/ResearchEyeCandy-1.jpg Publications Detail of the immersed mesh motion for the FSI 2 Hron & Turek fluid-structure interaction benchmark. Calculation made using the immersed finite element method. Calculation from S. Roy, L. Heltai, and F. Costanzo, "Benchmarking the immersed finite element method for fluid- structure interaction problems," Computer and Mathematics with Applications, 69 (2015), pp. 1167–1188. DOI: 10.1016/j.camwa.2015.03.012. The the details of numerical foundations of method are in L. Heltai and F. Costanzo, "Variational implementation of immersed finite element methods," Computer Methods in Applied Mechanics and Engineering, 229–232 (2012), pp. 110–127. DOI: 10.1016/j.cma.2012.04.001.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810b5bdb29d641ab687007/1501629277221/msc-evening-image.jpg Publications https://www.fmcostanzo.com/conference-proceedings-1 daily 0.75 2017-08-25 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Conference Proceedings Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f21ecbe6594169d41665e/1503601152177/ResearchEyeCandy-4.jpg Conference Proceedings Numerical prediction of the longitudinal component of the velocity of interstitial fluid flowing through brain tissue in response to the peristaltic motion of the wall of a typical penetrating artery in brain. The details of the numerical framework used for this calculation are in F. Costanzo and S. T. Miller, "An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory," Computer Methods in Applied Mechanics and Engineering, 323 (2017), pp. 64–97. DOI: 10.1016/j.cma.2017.05.006.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810b136f4ca3786e0e4a71/1501629204743/msc-evening-image.jpg Conference Proceedings https://www.fmcostanzo.com/conference-papers daily 0.75 2017-08-25 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f2187d2b8574d0435f2ba/1503601038237/ResearchEyeCandy-3.jpg Conference Presentations Streaming patterns near sharp edges in a miscroacoustofluidic channel. Among other things, this device configuration can be used a micropump, a micromixer, a microliquefier. Numerical and experimental details are in (i) N. Nama, P.-H. Huang, T. J. Huang, and F. Costanzo, "Investigation of acoustic streaming patterns around oscillating sharp edges," Lab on a Chip, 14 (2014), pp. 2824–2836. DOI: 10.1039/c4lc00191e; PMID: 24903475; PMCID: PMC4096312; (ii) N. Nama, P.-H. Huang, T. J. Huang, and F. Costanzo, ``Investigation of micromixing by acoustically oscillated sharp-edges,'' Biomicrofluidics, 10 (2016), pp. 024124–1–024124–17. DOI: 10.1063/1.4946875; PMID: 27158292; PMCID: PMC4833753.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Conference Presentations Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59810aafe3df287005ebcce5/1501629106070/msc-evening-image.jpg Conference Presentations https://www.fmcostanzo.com/service daily 0.75 2017-08-07 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Service Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/598219ac03596ef7a1665047/1501698477378/msc-evening-image.jpg Service https://www.fmcostanzo.com/profile-picture-name-email daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f3835cd0f681235cd8df4/1503606837868/ Profile Picture - w/Email Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Profile Picture - w/Email Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://www.fmcostanzo.com/profile-picture-name-only daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f380615d5dbb47b3f9e5d/1503606790880/ Profile Picture - Basic Francesco Costanzo, Ph.D. Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847441d482e94a17e8030c/59847460db29d66f894946f7/1503606790880/francesco-profile-image.jpg Profile Picture - Basic Francesco Costanzo, Ph.D. Download CV https://www.fmcostanzo.com/image-collections daily 0.75 2017-08-04 https://www.fmcostanzo.com/education-images daily 0.75 2017-08-22 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599c81a5f14aa1f9312f65dd/1503429029545/ Education Logos https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59846dfff9a61e76c6ee7cfa/59846e128419c27e055effde/1503429029545/politecnico-milano.jpg Education Logos https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59846dfff9a61e76c6ee7cfa/59846e4c1e5b6c1be8a73169/1503428996481/texas-a-and-m.jpg Education Logos Texas A&M University https://www.fmcostanzo.com/book-covers daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f39c7bebafbb13ba1c760/1503607134274/ Book Covers https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3f914e6bb95b91199a/1503607134274/statics.jpg Book Covers https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3e15d5db25d976f80a/1503607231387/dynamics.jpg Book Covers https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5988ad2715d5db25d976f632/5988ad3fbe65942a56757f92/1503607239146/statics-and-dynamics.jpg Book Covers https://www.fmcostanzo.com/key-achievements-6 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599ee91ef9a61e79d14e2cf9/1502198378345/ Key Achievements 6 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/5989ba68e45a7cfe22b1b8b1/1502198378345/KeyAchievements6-1.jpg Key Achievements 6 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8ac4c0dbf3e6afa27d0/1503586541111/KeyAchievements6-1.jpg Key Achievements 6 - Fig. 1 Idealized geometry of a vessel like the esophagus or an artery. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8b4ccc5c5e6c8ab6138/1503586567684/KeyAchievements6-2.jpg Key Achievements 6 - Fig. 2 Comparison between the nondimensional shear (μ) and effective shear (μeff) moduli for the Fung model for various values of λz and a = 0.5. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989ba56bebafbda588fdcc4/599ee8b8d2b85710609ab17d/1503586590807/KeyAchievements6-3.jpg Key Achievements 6 - Fig. 3 Comparison between the nondimensional shear (μ) and effective shear (μeff ) moduli for the Gent Model with λz = 1, I m = 500 and c2 /c1 = 1 , 1, 2. https://www.fmcostanzo.com/key-achievements-2 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599e17364c0dbf1bc7882e82/1502196673687/ Key Achievements 2 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/5989b3bc914e6b1524ba5891/1502196673687/KeyAchievements2-1.jpg Key Achievements 2 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaa69f8dce3deaf8f48b/1503532806408/KeyAchievements2-1.jpg Key Achievements 2 - Fig. 1 Microfluidic channel in a soft polymer actuated by surface acoustic waves. The surface acoustic waves leak energy into the polymer and microchannel and as a consequence, a pseudo-standing wave field arises. This field leads to acoustic streaming drag forces and radiation forces on suspended microparticles. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaaa579fb34211773af1/1503532835124/KeyAchievements2-2.jpg Key Achievements 2 - Fig. 2 ALE Formulation: magnitude of the Lagrangian-mean velocity (a) and of the Eulerian velocity (b) for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The lines represent the streamlines of the respective velocities. The Lagrangian velocity streamlines do not cross the channel walls, indicating no mass flow across the channel walls, while the Eulerian velocity streamlines cross the channel walls as though there were an outflow across the channel walls. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b3a446c3c4603303b967/599dcaadf9a61e30f52e566f/1503532853996/KeyAchievements2-3w.jpg Key Achievements 2 - Fig. 3 Ezb Formulation: magnitude of the (a) Lagrangian velocity and (b) Eulerian velocity for a device with dimensions comparable to the acoustic wavelength. The bottom wall is actuated. The Ezbc formulation (results in this figure) yields results that we believe are erroneous. The lines represent the streamlines of the respective velocities. Here the Lagrangian velocity streamlines cross the channel walls, indicating an unphysical mass flow across the channel walls. By contrast, consistent with the boundary conditions imposed in Ezbc formulation, here the Eulerian velocity streamlines do not cross the channel. These results are not supported by experimental evidence reported in Barnkob et al. (2016). https://www.fmcostanzo.com/key-achievements-5 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599e2040e9bfdfcc1bc0755a/1502197613253/ Key Achievements 5 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/5989b76ce45a7cfe22b1905c/1502197613253/KeyAchievements5-1.jpg Key Achievements 5 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fd7be42d6df90339fa6/1503535126599/KeyAchievements5-1.jpg Key Achievements 5 - Fig. 1 (a) Schematic of the device showing a microfluidic channel with sharp-edge structures on its side walls. The channel walls are subjected to a time-harmonic excitation produced by a piezoelectric transducer placed on one side of the channel. (b) Typical micro streaming patterns produced in the fluid occupying the channel as a response to piezoelectric excitation. (c) Typical geometric dimensions of the corrugated channel. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fde37c581435a2ab1b6/1503535149182/KeyAchievements5-2.jpg Key Achievements 5 - Fig. 2 Experimentally observed trajectories of 1.9 μm diameter fluorescent polystyrene beads in our acoustically oscillated micro-mixer with sharp edges. The geometry of the microchannel is described in Fig. 1(c) except for the fact that here, the tips of the sharp edges are 200 μm from the wall instead of 250 μm. The driven oscilla- tion is harmonic with a frequency equal to 4.75 kHz. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b75a6b8f5b32f3b22238/599e1fe3e45a7c310e02286d/1503535168598/KeyAchievements5-3.jpg Key Achievements 5 - Fig. 3 Plots of the velocity vbead in Eqn (20) corresponding to the boundary conditions in (a) eqn (14) and (b) eqn (15). The color map represents the magnitude of vbead whereas the lines are some of the streamlines of the vbead field. The channel dimensions are L = 300 μm (horizontal dimension), H = 600 μm (vertical dimension), α = 15° (sharp edge angle), and h = 200 μm (height of the sharp edge). The wall displacement was only in the vertical direction with magnitude 1 μm. https://www.fmcostanzo.com/key-achievements-1 daily 0.75 2017-08-23 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599dd998e6f2e1230cd23dbc/1502196422968/ Key Achievements 1 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/5989b2c5579fb3fb9606878d/1502196422968/KeyAchievements1-1.jpg Key Achievements 1 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a8fd4d2fa52d38a11/1503517043353/KeyAchievements1-1.jpg Key Achievements 1 - Method of Manufactured Solutions - 1 Magnitude of fluid velocity in a static evolution with stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3a59cc68d05673d40b/1503517056508/KeyAchievements1-2.jpg Key Achievements 1 - Method of Manufactured Solutions - 2 Magnitude of fluid velocity in a dynamic evolution without stabilization. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b29dbe65944f2a3d1cf3/599c9d3bf43b552f89f5643c/1503517080767/KeyAchievements1-3.png Key Achievements 1 - Method of Manufactured Solutions - 3 Convergence rates for the L2-norm of the error at t = 0.02s for a dynamic evolution without stabilization. https://www.fmcostanzo.com/key-achievements-4 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599f2bb0e4fcb5294d0f51d5/1502197311668/ Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/5989b63ef14aa1c7d2b8cd7c/1502197311668/KeyAchievements4-1.jpg Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2794ff7c5069b54ce453/1503602655311/p1_movie.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f27f0be6594169d420cd3/1503603631251/ok_tracks_01_um.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bbee58c624231843d67/1503603653546/ok_tracks_04_um.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bcdbe42d6c9ac3f430d/1503603664213/ok_tracks_08_um.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bf4f5e231b03da5fc66/1503603705708/actuation_movie_crop.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bd5be42d6c9ac3f43e4/1503603672664/ok_tracks_10_um.gif Key Achievements 4 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b62e86e6c050ffa4aec0/599f2bdfccc5c51d364466c5/1503603682762/ok_tracks_20_um.gif Key Achievements 4 https://www.fmcostanzo.com/key-achievements-3 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599e17776a4963803bb3f282/1503532884344/ Key Achievements 3 - Fig. 1 Configuration of 3D benchmark. The results of the simulation consists in tracking the displacement of the point A(t) in the figure and in determining the hydrodynamic forces acting on rigid obstacle and flexible bar system. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef14aa1072eb9ee15/1503532884344/KeyAchievements3-1.jpg Key Achievements 3 - Fig. 1 Configuration of 3D benchmark. The results of the simulation consists in tracking the displacement of the point A(t) in the figure and in determining the hydrodynamic forces acting on rigid obstacle and flexible bar system. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/5989b5204c0dbf9c31494a02/1502197025343/KeyAchievements3-1.jpg Key Achievements 3 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccef7e0abbcaa713df9/1503532901425/KeyAchievements3-2.jpg Key Achievements 3 - Fig. 2 Vertical channel containing viscous fluid through which a small incompressible disk is descending: (a) system’s geometry; (b) initial conditions (disk released from rest in a quiescent fluid); (c) detail of mesh of the immersed body. The disk’s terminal velocity is denoted by Ut. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/5989b4f903596e41d8c88745/599dcccee9bfdfdf306062a3/1503532919124/KeyAchievements3-3.jpg Key Achievements 3 - Fig. 3 Frame from animation showing the motion of a flexible flag as described in the FSI 2 benchmark by Hron and Turek. https://www.fmcostanzo.com/key-achievement-1-summary daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 1 Details - An Arbitrary Lagrangian–Eulerian FEM Formulation Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599dd7b8579fb34211784b23/1501626336829/msc-evening-image.jpg Key Achievement 1 Details - An Arbitrary Lagrangian–Eulerian FEM Formulation https://www.fmcostanzo.com/research-interests daily 0.75 2017-08-23 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599dde34b8a79ba9c1928bfb/1503518191785/ Research Interests - Fig 1 Numerical prediction of the radial component of the velocity of interstitial fluid relative to that of the tissue in response to the peristaltic motion of the wall of a typical penetrating artery in brain. This calculation is part of a study addressing an important open question in brain physiology: how are toxic metabolites cleared from brain tissue? When these metabolites accumulate in brain tissue various pathologies arise, including Alzheimer's disease. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0d6cd39c3b6a6035948/1503518191785/ResearchInterest-1.jpg Research Interests - Fig 1 Numerical prediction of the radial component of the velocity of interstitial fluid relative to that of the tissue in response to the peristaltic motion of the wall of a typical penetrating artery in brain. This calculation is part of a study addressing an important open question in brain physiology: how are toxic metabolites cleared from brain tissue? When these metabolites accumulate in brain tissue various pathologies arise, including Alzheimer's disease. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0db59cc68c69d2fa19b/1503518246898/ResearchInterest-2.jpg Research Interests - Fig. 2 Numerically predicted particle trajectories in a microacoustofluidic device in response to a high-frequency excitation of the substrate using surface acoustic waves. This calculation is part of a study to provide accurate engineering tools to design the next generation of diagnostic devices in biomedical applications. The devices are part of a growing technological trend called "lab-on-a-chip" (). This technology promises the ability to carry out in the palm of a hand a host of biochemical tests that nowadays require a well-equipped laboratory. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599dd0c73e00bef256add88f/599dd0deb8a79ba9c19175a7/1503518260035/ResearchInterest-3.jpg Research Interests - Fig. 3 Numerical prediction of the motion of a flexible tail flapping as fluids moves around it. This calculation is, which is part of a well-known benchmarking computational suite, was made to show that a new approach to solve fluid-structure interaction problems was indeed accurate and effective. Fluid-structure interaction is the study of the deformation of structures when they interact with a fluid in contact with them. The human body is a "gold-mine" of such problems. Here are just a few examples: blood flowing though flexible vasculature, food moving through the stomach and the intestine, brain pulsating while surrounded by cerebrospinal fluid. https://www.fmcostanzo.com/research-interests-details daily 0.75 2017-08-23 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Research Interests - Details Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599dde5abe6594a2d0e028a8/1501626336829/msc-evening-image.jpg Research Interests - Details https://www.fmcostanzo.com/key-achievements-7 daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599eebd53e00be7f96a2cbb5/1503587239221/ Key Achievements 7 - Fig. 1 - Key Result Key result of the paper: The discrete formulation has the same formal energy estimate as the abstract formulation. This result implies that the discrete formulation is stable.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb75f9a61e79d14e55b1/1503587239221/KeyAchievements7-1.jpg Key Achievements 7 - Fig. 1 - Key Result Key result of the paper: The discrete formulation has the same formal energy estimate as the abstract formulation. This result implies that the discrete formulation is stable.   https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb78f43b556c0c88ae12/1503587261745/KeyAchievements7-2.jpg Key Achievements 7 - Fig. 2 - Pressure Evolution A ball released in a fluid container and floating to the top: pressure evolution. https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/599eeb5ebe42d6838240640b/599eeb7a7131a589ecf50e4a/1503587285305/KeyAchievements7-3.jpg Key Achievements 7 - Fig. 3 - Velocity Evolution A ball released in a fluid container and floating to the top: velocity evolution. https://www.fmcostanzo.com/new-index daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 2 Details - Acoustic Streaming Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599eecf68fd4d2a2fdb432e9/1501626336829/msc-evening-image.jpg Key Achievement 2 Details - Acoustic Streaming https://www.fmcostanzo.com/key-achievement-4-details-numerical-study daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 4 Details - Numerical Study Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599ef6f8579fb3222f195a27/1501626336829/msc-evening-image.jpg Key Achievement 4 Details - Numerical Study https://www.fmcostanzo.com/key-achievement-3-details- daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 3 Details - Benchmarking FEM Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599eeecee9bfdf53aaf778ee/1501626336829/msc-evening-image.jpg Key Achievement 3 Details - Benchmarking FEM https://www.fmcostanzo.com/key-achievement-5-details- daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 5 Details - Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599ef6e87131a5d5ee66bc65/1501626336829/msc-evening-image.jpg Key Achievement 5 Details - https://www.fmcostanzo.com/key-achievement-6-details- daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 6 Details - Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599efc29cd0f687ac71c3d1e/1501626336829/msc-evening-image.jpg Key Achievement 6 Details - https://www.fmcostanzo.com/key-achievement-7-details- daily 0.75 2017-08-24 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Key Achievement 7 Details - Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/599efc12ff7c50af933a7f81/1501626336829/msc-evening-image.jpg Key Achievement 7 Details - https://www.fmcostanzo.com/service-editorship-reviewing daily 0.75 2017-08-25 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Service - Editorship & Reviewing Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59a0332d4c0dbf2616007977/1501626336829/msc-evening-image.jpg Service - Editorship & Reviewing https://www.fmcostanzo.com/service-workshops-conferences daily 0.75 2017-08-25 https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/59847477db29d66f8949480a/59847488914e6b93fcd1c4e8/1503606837868/francesco-profile-image.jpg Service - Workshops & Conferences Francesco Costanzo, Ph.D. Email: fmcostanzo@psu.edu Download CV https://static1.squarespace.com/static/596fe5cbf5e2319b746d6251/t/59a033c3914e6b856c53677f/1501626336829/msc-evening-image.jpg Service - 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