Статті в журналах: "Ventcel boundary conditions"

1

Lancia, Maria Rosaria, and Paola Vernole. "Semilinear Evolution Problems with Ventcel-Type Conditions on Fractal Boundaries." International Journal of Partial Differential Equations 2014 (January 22, 2014): 1–13. http://dx.doi.org/10.1155/2014/461046.

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A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface S or the corresponding prefractal interface Sh is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed.

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2

Cavalcanti, Marcelo M., Valéria N. Domingos Cavalcanti, Ryuichi Fukuoka, and Daniel Toundykov. "Stabilization of the damped wave equation with Cauchy–Ventcel boundary conditions." Journal of Evolution Equations 9, no. 1 (February 21, 2009): 143–69. http://dx.doi.org/10.1007/s00028-009-0002-1.

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3

Krasnoshchok, Mykola. "Dirihlet-Ventcel bounsdary problem for Laplace equation in an unbounded sector." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 37 (June 27, 2023): 24–37. http://dx.doi.org/10.37069/1683-4720-2023-37-3.

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We are concerned with boundary value problems for Laplace equation in an unbounded sector $s_\theta$ with vertex at the origin, the boundary conditions being of mixed type and jumping at corner. The boundary conditions are these: Dirichlet datum on one of the radial lines, while on the other the values of an Ventcel boundary condition is prescribed. We are interested in looking for solutions having a prescribed degree of smoothness up to the origin: more precisely we search for solutions of problem having all the derivatives up to the order that are square integrable with a power weight. This problem has a background in physical modeling of electrostatic or thermal imaging. Determining the geometry and the physical nature of an corrosion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation subject to appropriate boundary conditions on the corrosion surface. We are interesting in investigation of a regularity properties of solution to the @direct@ problem. Applying Mellin transform we pass to a finite difference equation.We use the methods of V.A.Solonnikov and E.V.Frolova just as in the case of the analogous finite difference equation obtained under the Dirichlet or the Neumann conditions indstead of the Ventcel condition in our case. We obtain the sulution of homogeneous difference equation in the form of infinite product. Then we find asymptotic formulas for this solution.Returning to nonhomogeneous differerence equation we find its solution in the form of contour integral. we define the solution of the starting problem by the help of the inverse Mellin transform. We estimate this solution in the norm of V.Kondratiev spaces $H^k_\mu(s_\theta$ under some conditions on weight $\mu$, higher order of derivatives $k$ and the opening of the angle $\theta$.

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4

Cavalcanti, Marcelo M., Ammar Khemmoudj, and Mohamed Medjden. "Uniform stabilization of the damped Cauchy–Ventcel problem with variable coefficients and dynamic boundary conditions." Journal of Mathematical Analysis and Applications 328, no. 2 (April 2007): 900–930. http://dx.doi.org/10.1016/j.jmaa.2006.05.070.

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5

Caubet, Fabien, Joyce Ghantous, and Charles Pierre. "A Priori Error Estimates of a Poisson Equation with Ventcel Boundary Conditions on Curved Meshes." SIAM Journal on Numerical Analysis 62, no. 4 (August 8, 2024): 1929–55. http://dx.doi.org/10.1137/23m1582497.

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6

Kanoune, A., and N. Mehidi. "Stabilization and control of subcritical semilinear wave equation in bounded domain with Cauchy-Ventcel boundary conditions." Applied Mathematics and Mechanics 29, no. 6 (June 2008): 787–800. http://dx.doi.org/10.1007/s10483-008-0610-x.

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7

Campiti, M., and G. Metafune. "Ventcel's boundary conditions and analytic semigroups." Archiv der Mathematik 70, no. 5 (May 1, 1998): 377–90. http://dx.doi.org/10.1007/s000130050210.

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8

Buffe, Rémi. "Stabilization of the wave equation with Ventcel boundary condition." Journal de Mathématiques Pures et Appliquées 108, no. 2 (August 2017): 207–59. http://dx.doi.org/10.1016/j.matpur.2016.11.001.

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9

Zeng, Yi, and Yousong Luo. "Linear parabolic equations with venttsel initial boundary conditions." Bulletin of the Australian Mathematical Society 50, no. 3 (December 1994): 465–79. http://dx.doi.org/10.1017/s0004972700013587.

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The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.

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10

Luo, Yousong, and Neil S. Trudinger. "Linear second order elliptic equations with Venttsel boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 118, no. 3-4 (1991): 193–207. http://dx.doi.org/10.1017/s0308210500029048.

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SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

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11

Luo, Yousong, and Neil S. Trudinger. "Quasilinear second order elliptic equations with Venttsel boundary conditions." Potential Analysis 3, no. 2 (June 1994): 219–43. http://dx.doi.org/10.1007/bf01053434.

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12

Nicaise, Serge, and Karima Laoubi. "Polynomial stabiization of the wave equation with Ventcel's boundary conditions." Mathematische Nachrichten 283, no. 10 (July 9, 2010): 1428–38. http://dx.doi.org/10.1002/mana.200710162.

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13

Luo, Yousong. "Necessary Optimality Conditions for Some Control Problems of Elliptic Equations with Venttsel Boundary Conditions." Applied Mathematics and Optimization 61, no. 3 (September 15, 2009): 337–51. http://dx.doi.org/10.1007/s00245-009-9087-8.

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14

Lancia, Maria Rosaria, Alejandro Vélez-Santiago, and Paola Vernole. "Quasi-linear Venttsel’ problems with nonlocal boundary conditions on fractal domains." Nonlinear Analysis: Real World Applications 35 (June 2017): 265–91. http://dx.doi.org/10.1016/j.nonrwa.2016.11.002.

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15

Clément, Ph, and C. A. Timmermans. "On C0-semigroups generated by differential operators satisfying Ventcel's boundary conditions." Indagationes Mathematicae (Proceedings) 89, no. 4 (1986): 379–87. http://dx.doi.org/10.1016/1385-7258(86)90023-5.

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16

Amosov, Andrey, and Nikita Krymov. "On a Nonlinear Initial—Boundary Value Problem with Venttsel Type Boundary Conditions Arizing in Homogenization of Complex Heat Transfer Problems." Mathematics 10, no. 11 (May 31, 2022): 1890. http://dx.doi.org/10.3390/math10111890.

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We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regularity of a weak solution v. We obtained estimates for the derivatives Dtv, D12v, D22v, D1D2v with a qualified order in the small parameter ε.

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17

Badra, Mehdi, and Takéo Takahashi. "Analyticity of the semigroup corresponding to a strongly damped wave equation with a Ventcel boundary condition." Dynamics of Partial Differential Equations 20, no. 3 (2023): 249–62. http://dx.doi.org/10.4310/dpde.2023.v20.n3.a5.

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18

Bonnaillie-Noël, V., M. Dambrine, F. Hérau, and G. Vial. "On Generalized Ventcel's Type Boundary Conditions for Laplace Operator in a Bounded Domain." SIAM Journal on Mathematical Analysis 42, no. 2 (January 2010): 931–45. http://dx.doi.org/10.1137/090756521.

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19

Boudrahem, Nassim, and Ahmed Berboucha. "Theoretical justification of Ventcel's boundary conditions for a thin layer three-dimensional thermoelasticity problem." Miskolc Mathematical Notes 22, no. 2 (2021): 581. http://dx.doi.org/10.18514/mmn.2021.3679.

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20

Shen, Zhigang, and Shimin Wang. "INVESTIGATING SELF-COOLING EFFECTS OF VENTILATED ATTICS UNDER DIFFERENT ROOF AND AMBIENT TEMPERATURES IN SUMMER." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 20, no. 5 (July 4, 2014): 674–85. http://dx.doi.org/10.3846/13923730.2013.802738.

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An unsteady computational fluid dynamics model is employed to simulate summer-time buoyancy-driven turbulent ventilation in gable-roof attics of residential buildings. The energy performance of vented attics is assessed by comparing their performance to sealed attics with the same geometry and insulation configurations. The simulated boundary conditions of the roof-top temperature ranging between 295.15 K and 345.15 K, coupled with an ambient temperature ranging between 295.15 K and 315.15 K, resemble the summer attic conditions with effects of solar irradiance on the roofs. Simulation results indicate that both the vented and sealed attics are dominated by thermal stratification. The cooling load of the sealed attic is predicted to be about 3 times greater than that of the vented attic for a roof-top temperature of 345.15 K and an ambient temperature of 305.15 K. Both the cooling load and ventilating air flow rate of the vented attic are sensitive to the ambient temperature variation.

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21

Du, Z. G., and E. Bilgen. "Effects of Heat Intensity, Size, and Position of the Components on Temperature Distribution Within an Electronic PCB Enclosure." Journal of Electronic Packaging 112, no. 3 (September 1, 1990): 249–54. http://dx.doi.org/10.1115/1.2904374.

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Natural convection heat transfer has been studied in a sealed small PCB enclosure of three heated components which are mounted on a PCB plate within a large console cooled by vented airflow. A two-dimensional laminar flow model is used with appropriate boundary conditions. Detailed influences of each parameter, such as intensity, size, and position of the heaters on temperature and flow distributions within the enclosure have been studied. The favorable component arrangements for various cases have been determined.

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22

Mahaffey, J. W., R. J. Diederich, and T. C. Kaufman. "Novel patterns of homeotic protein accumulation in the head of the Drosophila embryo." Development 105, no. 1 (January 1, 1989): 167–74. http://dx.doi.org/10.1242/dev.105.1.167.

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Antibodies that specifically recognize proteins encoded by the homeotic genes: Sex combs reduced, Deformed, labial and proboscipedia, were used to follow the distribution of these gene products during embryogenesis. The position of engrailed-expressing cells was used as a reference and staining conditions were established that could distinguish, among cells expressing engrailed, one of the homeotic proteins or both. Our observations demonstrate two important facts about establishing identity in the head segments. First, in contrast to the overlapping pattern of homeotic gene expression in the trunk segments, we observe a non-overlapping pattern in the head for those homeotic proteins required during embryogenesis. In contrast, the spatial accumulation of the protein product of the non-vital proboscipedia locus overlaps partially with the distribution of the Deformed and Sex combs reduced proteins in the maxillary and labial segments, respectively. Second, two of the proteins, Sex combs reduced and Deformed, have different dorsal and ventral patterns of accumulation. Dorsally, these proteins are expressed in segmental domains while, within the ventral region, a parasegmental register is observed. The boundary where this change in pattern occurs coincides with the junction between the ventral neurogenic region and the dorsal epidermis. After contraction of the germ band, when the nerve cord has completely separated from the epidermis, the parasegmental pattern is observed only within the ventral nerve cord while a segmental register is maintained throughout the epidermis.

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23

Fontanet, Joan, Luis E. Herranz, Alastair Ramlakan, and Lolan Naicker. "Modelling of HTR Confinement Behaviour during Accidents Involving Breach of the Helium Pressure Boundary." Science and Technology of Nuclear Installations 2009 (2009): 1–11. http://dx.doi.org/10.1155/2009/687634.

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Development of HTRs requires the performance of a thorough safety study, which includes accident analyses. Confinement building performance is a key element of the system since the behaviour of aerosol and attached fission products within the building is of an utmost relevance in terms of the potential source term to the environment. This paper explores the available simulation capabilities (ASTEC and CONTAIN codes) and illustrates the performance of a postulated HTR vented confinement under prototypical accident conditions by a scoping study based on two accident sequences characterized by Helium Pressure Boundary breaches, a small and a large break. The results obtained indicate that both codes predict very similar thermal-hydraulic responses of the confinement both in magnitude and timing. As for the aerosol behaviour, both codes predict that most of the inventory coming into the confinement is eventually depleted on the walls and only about 1% of the aerosol dust is released to the environment. The crosscomparison of codes states that largest differences are in the intercompartmental flows and the in-compartment gas composition.

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24

Liu, Xiang-Long, Guang-Cai Gong, Heng-Sheng Cheng, and Li-Xing Ding. "Airflow and Heat Transfer in the Slot-Vented Room with Radiant Floor Heating Unit." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/287271.

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Radiant floor heating has received increasing attention due to its diverse advantages, especially the energy saving as compared to the conventional dwelling heating system. This paper presents a numerical investigation of airflow and heat transfer in the slot-vented room with the radiant floor heating unit. Combination of fluid convection and thermal radiation has been implemented through the thermal boundary conditions. Spatial distributions of indoor air temperature and velocity, as well as the heat transfer rates along the radiant floor and the outer wall, have been presented and analyzed covering the domains from complete natural convection to forced convection dominated flows. The numerical results demonstrate that the levels of average temperature in the room with lateral slot-ventilation are higher than those without slot-ventilation, but lower than those in the room with ceiling slot-ventilation. Overall, the slot-ventilation room with radiant floor heating unit could offer better indoor air quality through increasing the indoor air temperature and fresh air exchanging rate simultaneously. Concerning the airborne pollutant transports and moisture condensations, the performance of radiant floor heating unit will be further optimized in our future researches.

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25

Henne, Stephan, Markus Furger, and AndréS H. Prévôt. "Climatology of Mountain Venting–Induced Elevated Moisture Layers in the Lee of the Alps." Journal of Applied Meteorology 44, no. 5 (May 1, 2005): 620–33. http://dx.doi.org/10.1175/jam2217.1.

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Abstract Elevated moisture layers in the lower free troposphere (2000–6000 m MSL) in the lee of the Alps were investigated. Specific humidity was analyzed within a Lagrangian concept for fair-weather days during a 12-yr period at the windward and the leeward sides of the Alps for the sounding sites of Payerne, Switzerland, and Milan, Italy. During daytime fair-weather conditions (different criteria), specific humidity increased significantly in air masses that advected from Payerne to Milan in a layer ranging from ∼2500 to 4000 m MSL. The maximum relative increase of specific humidity in this layer was ∼0.3, meaning that ∼30% of the air in this layer originated from the Alpine atmospheric boundary layer. On average, ∼30% of the mass of the Alpine boundary layer was vented to altitudes higher than 2500 m MSL per hour during the daytime. The total precipitable water within a layer reaching from 2500 to 3500 m MSL increased by ∼1.3 mm. Similar elevated layers were observed for different selection methods of fair-weather days, and climatologically for the whole of June, July, and August. Average observations of the relative increase and boundary layer export rate agree with results from the local case studies. Daytime thermally driven flow systems seem to be the main source of additional water vapor in the observed elevated layers over the Alps. Subsequently, horizontal advection toward flat terrain where the average ABL top was well below the elevated layer bottom results in the export of ABL air to the free troposphere (mountain venting). Mountain venting was enhanced in situations with larger global radiation, lower atmospheric stability, and additional moist convection as was detected by lightning activity.

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26

Crônier, Catherine, Petr Budil, Oldřich Fatka, and Lukáš Laibl. "Intraspecific bimodal variability in eye lenses of two Devonian trilobites." Paleobiology 41, no. 4 (September 2015): 554–69. http://dx.doi.org/10.1017/pab.2015.29.

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AbstractArthropods are known to display a variable number of eye lenses and this number mostly increases during their development. In trilobites, most species possessing schizochroal eyes exhibit a notable intraspecific variation in the number of dorso ventral files of eye lenses that can be age related (i.e., growth) or not (i.e., living environment). Several previous studies have shown that some trilobite groups (e.g. phacopids) tend to have fewer lenses/files in representatives from the deeper habitats than those from shallower habitats. In this study, we analyzed the pattern of variation in the number of dorso ventral files of eye lenses in two Devonian phacopid trilobites from the Prague Basin of the Czech Republic. We quantified their intraspecific variability. To better understand the patterning, we compared more than 120 individuals. Data first reveal evidence of a bimodal distribution of lens/file number without intermediate forms among each of two studied populations ofProkops prokopi(Chlupáč, 1971) and throughout the ontogeny ofPedinopariops insequens(Chlupáč, 1977). Our results indicate that caution must be taken for taxonomical affiliation and biodiversity analyses of taxa in which the intraspecific variability is unclear. Additionally, we investigated possible relations of these bimodalities to the stratigraphical position of studied populations and to the paleoenvironment. InProkops prokopi, a slightly different age of both populations, together with supposed differences in the local environments can be responsible for observed variability. InPedinopariops insequens, stress conditions possibly related to the approaching onset of the Basal Choteč Event can be responsible for surprising intrapopulation variability. We speculate that the stress conditions could cause a bimodal selection and possibly also the change of ontogenetic trajectory within this species.Pedinopariops insequenswas the only phacopid in the Prague Basin that crosses the Lower/Middle Devonian boundary and survived also the onset of Basal Choteč Event.

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27

Kosma, Madison M., Alexander J. Werth, Andrew R. Szabo, and Janice M. Straley. "Pectoral herding: an innovative tactic for humpback whale foraging." Royal Society Open Science 6, no. 10 (October 2019): 191104. http://dx.doi.org/10.1098/rsos.191104.

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Humpback whales ( Megaptera novaeangliae ) have exceptionally long pectorals (i.e. flippers) that aid in shallow water navigation, rapid acceleration and increased manoeuvrability. The use of pectorals to herd or manipulate prey has been hypothesized since the 1930s. We combined new technology and a unique viewing platform to document the additional use of pectorals to aggregate prey during foraging events. Here, we provide a description of ‘pectoral herding’ and explore the conditions that may promote this innovative foraging behaviour. Specifically, we analysed aerial videos and photographic sequences to assess the function of pectorals during feeding events near salmon hatchery release sites in Southeast Alaska (2016–2018). We observed the use of solo bubble-nets to initially corral prey, followed by calculated movements to establish a secondary boundary with the pectorals—further condensing prey and increasing foraging efficiency. We found three ways in which humpback whales use pectorals to herd prey: (i) create a physical barrier to prevent evasion, (ii) cause water motion to guide prey towards the mouth, and (iii) position the ventral side to reflect light and alter prey movement. Our findings suggest that behavioural plasticity may aid foraging in changing environments and shifts in prey availability. Further study would clarify if ‘pectoral herding’ is used as a principal foraging tool by the broader humpback whale population and the conditions that promote its use.

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28

Grant, Jonathan, Craig W. Emerson, and Sandra E. Shumway. "Orientation, passive transport, and sediment erosion features of the sea scallop Placopecten magellanicus in the benthic boundary layer." Canadian Journal of Zoology 71, no. 5 (May 1, 1993): 953–59. http://dx.doi.org/10.1139/z93-125.

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Passive transport and orientation of sea scallops (Placopecten magellanicus; 27–120 mm shell height) were studied in a laboratory flume to assess flow-mediated control of movement and position on the seabed. Additional experiments were conducted to characterize patterns of sediment transport around the scallop shell in relation to recesses occupied by scallops. The critical shear velocity of scallop transport was not correlated with shell height or other size measures, and most scallops were transported with the ventral shell margin facing downstream. Frontal exposure of scallops to the flow as indicated by fineness (shell height/shell depth) was greater in larger scallops, but when pallial gape was included in fineness (shell height/shell depth + gape)), frontal exposure was not correlated with scallop size. This suggests that variation in the drag component of transport was responsible for the lack of correlation between shell morphometry and critical shear velocity. Sediment transport created a horseshoe-shaped trough around the shell and several smaller erosion–deposition features downstream. The dimensions of sediment transport features were dependent on shell allometry, and it is likely that sediment transport contributes to the formation of scallop recesses typically observed in scallop beds. These results indicate that passive transport of sea scallops has a behavioural component related to gape that is independent of shell size. In contrast, scallop orientation and recessing may be explained by physical processes rather than simply by behaviour. Studies of bivalve hydrodynamics require consideration of living animals in addition to shell specimens and must include conditions of benthic boundary layer flow and sediment transport.

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Bochkarev, D. V., Yu N. Nedayborshch, A. N. Nikolskiy, A. N. Slugin, and V. D. Bochkarev. "EVOLUTION OF WEED FLORA IN SUGAR BEET CROPS UNDER DIFFERENT DEGREESOF ANTHROPOGENIC LOAD IN THE 20TH CENTURY AND EARLY 21STCENTURY." Vestnik Altajskogo gosudarstvennogo agrarnogo universiteta, no. 10 (2021): 5–12. http://dx.doi.org/10.53083/1996-4277-2021-204-10-5-12.

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The south of the Non-Chernozem Region is the north-ern boundary of sugar beet production in the Russian Fed-eration. An important factor restraining the growth of crop productivity is the high weed infestation of crops. To devel-op an effective system of crop protection against weeds, it is necessary to study their species composition in order to determine the most occurring and noxious weed species. The available data of geobotanical surveys since the 1930s showed that at different levels of anthropogenic impact the core of the most noxious weed species was formed. Under extensive agriculture conditions, the following species were the most widespread ones: Elytrigia repens(L.) Nevski, Equiseeum arvenseL., Sonchus arvensis L., Convolvulus arvensisL., Cirsium setosum(Willd.) Besser., Artemisia absinthiumL., Chenopodium albumL., Polygonum avicula-reL., Apera spica-ventiL., etc. The introduction of mechan-ical plowing decreased the population density of A. spica-ventiL., Dracocephalum thymiflorumL., and P. aviculareL. Further intensification of agriculture contributed to the narrowing of the weed species composition. Avena fatuaL., not previously found, appeared in abundance in crops and surpassed all other species in terms of number and frequency of occurrence, as well as species resistant to herbicides from the 2.4-D dimethylamine group -Poaceae, Galium aparineL., Tripleurospermum inodorum(L.) Sch. Bip. Couch grass(Elytrigia repens(L.) Nevski) was com-pletely substituted. Currently, the agrophytocenoses con-tain the most harmful rhizome and root-sucker weeds and spring species. Thefollowing early spring weeds are par-ticularly harmful and highly spread in crops: common wild oat (Avena fatuaL.), hemp-nettle species (Galeopsis), and Chenopodium albumL.; overwintering weeds resistant to 2.4-D dimethylamine which seeds accumulate in the soil during the cultivation of other crops in crop rotations where weed control is not so intense.

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Dubovik, S. A. "Asymptotic Semantization of Data in Control Systems." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 8 (August 8, 2019): 461–71. http://dx.doi.org/10.17587/mau.20.461-471.

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Asymptotic methods for analyzing large deviations in this work are used to convert information about the state of a controlled diffusion process into probabilistic estimates of the normal or abnormal development of the process. Thus, over the reflex contour of local stabilization a system of global semantic control is implemented, a kind of second signal system. A functional analytical approach similar to the weak convergence of probabilistic measures is used as an analysis tool, which makes it possible to significantly expand the conditions for applying the method. Global control is reduced to solving the Lagrange problem in the form of Pontryagin for the system of ordinary differential equations (system of paths), the Ventzel-Freidlin action functional (or "rate function" in some English literature), which is presented here as an integral-quadratic criterion for control functions in the system of paths, and the boundary condition in the form of the critical state of the system. A bounded solution of the Lagrange — Pontryagin problem on the half-line, which gives a prototype of the quasipotential of the system of paths, is called the A-profile of the critical state. The A-profile makes it possible to significantly simplify the procedure for analyzing large deviations, up to its implementation in real time and the implementation of the global control loop (2nd signaling system). The resulting two-tier architecture is positioned as a baseline to achieve the functional stability of the control system. It is speculated that this role of the apparatus of large deviations takes place in biological evolving systems, including the formation of languages and other attributes of the evolution of higher human nervous activity.

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31

Natu, Vaidehi S., Jesse Gomez, Michael Barnett, Brianna Jeska, Evgeniya Kirilina, Carsten Jaeger, Zonglei Zhen, et al. "Apparent thinning of human visual cortex during childhood is associated with myelination." Proceedings of the National Academy of Sciences 116, no. 41 (September 23, 2019): 20750–59. http://dx.doi.org/10.1073/pnas.1904931116.

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Human cortex appears to thin during childhood development. However, the underlying microstructural mechanisms are unknown. Using functional magnetic resonance imaging (fMRI), quantitative MRI (qMRI), and diffusion MRI (dMRI) in children and adults, we tested what quantitative changes occur to gray and white matter in ventral temporal cortex (VTC) from childhood to adulthood, and how these changes relate to cortical thinning. T1 relaxation time from qMRI and mean diffusivity (MD) from dMRI provide independent and complementary measurements of microstructural properties of gray and white matter tissue. In face- and character-selective regions in lateral VTC, T1 and MD decreased from age 5 to adulthood in mid and deep cortex, as well as in their adjacent white matter. T1 reduction also occurred longitudinally in children’s brain regions. T1 and MD decreases 1) were consistent with tissue growth related to myelination, which we verified with adult histological myelin stains, and 2) were correlated with apparent cortical thinning. In contrast, in place-selective cortex in medial VTC, we found no development of T1 or MD after age 5, and thickness was related to cortical morphology. These findings suggest that lateral VTC likely becomes more myelinated from childhood to adulthood, affecting the contrast of MR images and, in turn, the apparent gray–white boundary. These findings are important because they suggest that VTC does not thin during childhood but instead gets more myelinated. Our data have broad ramifications for understanding both typical and atypical brain development using advanced in vivo quantitative measurements and clinical conditions implicating myelin.

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32

Rossion, Bruno, Christine Schiltz, Laurence Robaye, David Pirenne, and Marc Crommelinck. "How Does the Brain Discriminate Familiar and Unfamiliar Faces?: A PET Study of Face Categorical Perception." Journal of Cognitive Neuroscience 13, no. 7 (October 1, 2001): 1019–34. http://dx.doi.org/10.1162/089892901753165917.

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Where and how does the brain discriminate familiar and unfamiliar faces? This question has not been answered yet by neuroimaging studies partly because different tasks were performed on familiar and unfamiliar faces, or because familiar faces were associated with semantic and lexical information. Here eight subjects were trained during 3 days with a set of 30 faces. The familiarized faces were morphed with unfamiliar faces. Presented with continua of unfamiliar and familiar faces in a pilot experiment, a group of eight subjects presented a categorical perception of face familiarity: there was a sharp boundary in percentage of familiarity decisions between 40% and 60% faces. In the main experiment, subjects were scanned (PET) on the fourth day (after 3 days of training) in six conditions, all requiring a sex classification task. Completely novel faces (0%) were presented in Condition 1 and familiar faces (100%) in Condition 6, while faces of steps of 20% in the continuum of familiarity were presented in Conditions 2 to 5 (20% to 80%). A principal component analysis (PCA) indicated that most variations in neural responses were related to the dissociation between faces perceived as familiar (60% to 100%) and faces perceived as unfamiliar (0 to 40%). Subtraction analyses did not disclose any increase of activation for faces perceived as familiar while there were large relative increases for faces perceived as unfamiliar in several regions of the right occipito-temporal visual pathway. These changes were all categorical and were observed mainly in the right middle occipital gyrus, the right posterior fusiform gyrus, and the right inferotemporal cortex. These results show that (1) the discrimination between familiar and unfamiliar faces is related to relative increases in the right ventral pathway to unfamiliar/novel faces; (2) familiar and unfamiliar faces are discriminated in an all-or-none fashion rather than proportionally to their resemblance to stored representations; and (3) categorical perception of faces is associated with abrupt changes of brain activity in the regions that discriminate the two extremes of the multidimensional continuum.

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Schuschnig, Uwe, Ashley Norris Weigand, Manfred Keller, Klopfer Elisabeth, Axel Krüner, and Martin Luber. "R458 – Drug Delivery to the Sinuses- Basics and Aerosol Dynamics." Otolaryngology–Head and Neck Surgery 139, no. 2_suppl (August 2008): P198. http://dx.doi.org/10.1016/j.otohns.2008.05.617.

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Problem Drug delivery to the sinuses via aerosols appears to be a very difficult task, since the paranasal cavities are virtually non-vented cavities. However, there is a scientifically traceable approach to transport aerosol to the sinuses via pressure differences using so-called “vibrating” or “sonic” aerosols which suggests that pressure fluctuations increase aerosol diffusion and ventilate dead spaces by flow induction. Methods The influence of droplet size, vibration frequency and flow rate on drug delivery to the nasal and paranasal cavities was studied in a human nasal cast model (NC). One ml of a Levofloxacin solution (100 mg/ml) was aerosolized into the NC by a VibrENT prototype nebulizer generating a slow, high density aerosol (MMD = 3.7μm) via a perforated vibrating membrane in connection with an adjustable pulsation source. Results Total paranasal cavity deposition was highest (-20 % of label claim) configured with ostia of 1 and 3 mm in diameter and sinus volumes of 7, 12 and 23 ml when VibrENT was operated at flow rates below 3 1/min and a pulsation frequency of 36 Hz. Delivery efficiency decreased at higher frequencies, higher flow rates and with larger aerosol droplets. Omission of pulsation resulted in no paranasal deposition and a drop in nasal cavity deposition from more than 50% to about 6%. Drug deposition to the sinuses is also significantly (p<0.01) affected by the ostium diameter and sinus volume, being lowest (∼0.2 %) at a large ostium diameter (6 mm) and a low sinus volume (7 ml). Conclusion It is possible to deliver aerosol to the sinuses but physical boundary conditions like pulsation frequency, aerosol size and flow rate have to be considered for an efficient transport as well as sinus anatomy. PARI VibrENT addresses these requirements. Significance Efficient drug transport to the sinuses enables novel therapeutic approaches.

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Hoang, Thi-Thao-Phuong. "Optimized Ventcel-Schwarz waveform relaxation and mixed hybrid finite element method for transport problems." Discrete & Continuous Dynamical Systems - S, 2022, 0. http://dx.doi.org/10.3934/dcdss.2022060.

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<p style='text-indent:20px;'>This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both diffusive and advective flux, and Lagrange multipliers are introduced on the interfaces between nonoverlapping subdomains to handle tangential derivatives in the Ventcel conditions. A space-time interface problem is formulated and is solved iteratively. Each iteration involves the solution of time-dependent problems with Ventcel boundary conditions in the subdomains. The subdomain problems are discretized in space by a mixed hybrid finite element method based on the lowest-order Raviart-Thomas space and in time by the backward Euler method. The proposed algorithm is fully implicit and enables different time steps in the subdomains. Numerical results with discontinuous coefficients and various Peclét numbers validate the accuracy of the method with nonconforming time grids and confirm the improved convergence properties of Ventcel conditions over Robin conditions.</p>

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Almeida, A. F., M. M. Cavalcanti, V. H. Gonzalez Martinez, and J. P. Zanchetta. "Uniform stabilization for the semilinear wave equation in an inhomogeneous medium with locally distributed nonlinear damping and dynamic Cauchy–Ventcel type boundary conditions." Communications in Contemporary Mathematics, October 11, 2019, 1950072. http://dx.doi.org/10.1142/s021919971950072x.

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In this paper, we consider the Cauchy–Ventcel problem in an inhomogeneous medium with dynamic boundary conditions subject to a nonlinear damping distributed around a neighborhood [Formula: see text] of the boundary according to the Geometric Control Condition. Uniform decay rates of the associated energy are established and, in addition, the exact internal controllability for the linear problem is also proved. For this purpose, refined microlocal analysis arguments are considered by exploiting ideas due to Burq and Gérard [Contrôle Optimal des équations aux dérivées partielles. (2001); http://www.math.u-psud.fr/burq/articles/coursX.pdf ].

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Takahashi, Takéo, and Rémi Buffe. "Controllability of a Stokes system with a diffusive boundary condition." ESAIM: Control, Optimisation and Calculus of Variations, September 12, 2022. http://dx.doi.org/10.1051/cocv/2022057.

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We are interested by the controllability of a fluid-structure interaction system where the fluid is viscous and incompressible and where the structure is elastic and located on a part of the boundary of the fluid's domain. In this article, we simplify this system by considering a linearization and by replacing the wave/plate equation for the structure by a heat equation. We show that the corresponding system coupling the Stokes equations with a heat equation at its boundary is null-controllable. The proof is based on Carleman estimates and interpolation inequalities. One of the Carleman estimates corresponds to the case of Ventcel boundary conditions. This work can be seen as a first step to handle the real system where the structure is modeled by the wave or the plate equation.

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Simion Antunes, José G., Marcelo M. Cavalcanti, and Valéria N. Domingos Cavalcanti. "Uniform decay rate estimates for the 2D wave equation posed in an inhomogeneous medium with exponential growth source term, locally distributed nonlinear dissipation, and dynamic Cauchy–Ventcel–type boundary conditions." Mathematische Nachrichten, October 3, 2023. http://dx.doi.org/10.1002/mana.202200288.

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AbstractWe study the wellposedness and stabilization for a Cauchy–Ventcel problem in an inhomogeneous medium with dynamic boundary conditions subject to a exponential growth source term and a nonlinear damping distributed around a neighborhood ω of the boundary according to the geometric control condition. We, in particular, generalize substantially the work due to Almeida et al. (Commun. Contemp. Math. 23 (2021), no. 03, 1950072), in what concerns an exponential growth for source term instead of a polynomial one. We give a proof based on the truncation of a equivalent problem and passage to the limit in order to obtain in one shot, the energy identity as well as the observability inequality, which are the essential ingredients to obtain uniform decay rates of the energy. We show that the energy of the equivalent problem goes uniformly to zero, for all initial data of finite energy taken in bounded sets of finite energy phase space. One advantage of our proof is that the decay rate is independent of the nonlinearity.

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38

Campiti, Michele. "Second-Order Differential Operators with Non-Local Ventcel's Boundary Conditions." Constructive Mathematical Analysis, December 1, 2019, 144–52. http://dx.doi.org/10.33205/cma.574194.

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Addoun, Rayan Ikram, and K. Laoubi. "Stability and regularity analysis of nonlinear wave equations with localised internal and Ventcell boundary conditions." International Journal of Control, July 4, 2024, 1–10. http://dx.doi.org/10.1080/00207179.2024.2368052.

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Ulrich, Martin, Filip Niemann, and Georg Grön. "Role of the right anterior insula for the emergence of flow—A combined task-based fMRI activation and connectivity study." Frontiers in Human Neuroscience 16 (December 8, 2022). http://dx.doi.org/10.3389/fnhum.2022.1067968.

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The emergence of flow is a situation of high salience because externally oriented attention on the task and access to resources for goal-directed behavior are enhanced, while internally oriented or self-related cognition is decreased. The right anterior insula has been reported as a causal out-flow hub of the salience resting-state network, orchestrating the engagement of the central executive network (CEN) and the disengagement of the default-mode network (DMN) during a functional challenge. In the present study, we employed a combined task-based activation and connectivity analysis to investigate the role of the right anterior insula during the emergence of flow. A sample of 41 healthy male subjects was confronted with a functional challenge that permitted the emergence of flow during BOLD-based functional magnetic resonance imaging. Comparing connectivity changes in the right anterior insula during the flow condition against connectivity changes associated with control conditions of boredom and overload, relatively increased couplings were observed with the left and right dorsolateral prefrontal cortex. Activation data for these regions did, however, not show the flow-typical inverted U-shaped (invU) response pattern. Relatively decreased functional couplings encompassed ventral aspects of the striatum, but neither the amygdala nor the medial prefrontal cortex (MPFC). For the ventral striatum, activation data were consistent with the flow-typical U-shaped activation pattern, which supports the notion that under the high salience of autotelic situations, the anterior insula is much less positively coupled with the ventral striatum than under boundary conditions of boredom and overload. Taken together, present functional connectivity results were in alignment with the assumed role of the right anterior insula under conditions of different salience. However, this particular region does not appear to mediate the most typical flow-associated activation patterns.

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41

Roy, Nepal Chandra. "Combustion of a nanoparticles-laden chemical in a vented cavity." Physics of Fluids 36, no. 3 (March 1, 2024). http://dx.doi.org/10.1063/5.0196344.

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Mixed convective characteristics of the combustion of a nanoparticles-laden fuel (n-butanol nanofluid) in a vented cavity are investigated. The nanofluid and the oxidizer enter the cavity through the inlets on the left and right vertical walls, respectively. However, the resulting product produced from the oxidation process of the fuel exits the cavity through the outlet at the bottom wall. Heat generated from the oxidation process causes natural convection within the cavity. The conjugate effect of natural and forced convection finally gives rise to mixed convection phenomena. In this regard, a mathematical model for mixed convection flow in a vented cavity is formulated with no-slip and isothermal boundary conditions. Having transformed the model into a dimensionless form, the stream function-vorticity formulation is used. The resulting equations are then solved numerically using the finite difference method. Numerical results are illustrated with the streamlines, isotherms, and isolines of fuel and oxidizer concentrations. The maximum values of the stream function (ψmax) and the temperature (θmax) are found to increase with an increase in the Frank–Kamenetskii number (Λ), volume fraction of nanoparticles (φ), and stoichiometric ratio (χ). On the contrary, they decrease with the increase in the Reynolds number (Re). When the Grashof number (Gr) is increased, ψmax increases and θmax decreases. The remaining concentrations of fuel, (CF)min, and oxidizer, (CO)min, are higher for an increase in Gr, whereas the opposite is recognized for increasing Λ. With the increase in Gr and Λ, the steady-state flow in the cavity tends to be oscillating and then chaotic.

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Bustard, Andrew N., Mark E. Noftz, Mitsugu Hasegawa, Hirotaka Sakaue, Joseph S. Jewell, Nicholas J. Bisek, and Thomas J. Juliano. "Dynamics of a 3-D inlet/isolator measured with fast pressure-sensitive paint." Experiments in Fluids 65, no. 7 (July 2024). http://dx.doi.org/10.1007/s00348-024-03836-7.

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AbstractFast pressure-sensitive paint (PSP) was applied to an inlet/isolator designed using the Osculating Internal Waverider Inlet with Parallel Streamlines (OIWPS) method. The dorsal isolator surface pressure was measured using anodized-aluminum PSP through transparent cast acrylic that makes up the ventral portion of the isolator. Temperature-sensitive paint was utilized to correct for the PSP’s temperature sensitivity. The model was tested under Mach 5.7 flow at Re $$=$$ = 8.5 $$\times 10^6$$ × 10 6 /m and 10.2 $$\times 10^6$$ × 10 6 /m in the AFOSR–Notre Dame Large Mach-6 Quiet Tunnel (ANDLM6QT) under conventional noise conditions. Flow phenomena, such as shocks originating in the inlet and flow separation at the throat, were visualized with high spatial resolution. The dynamics measured by the PSP and pressure transducers matched well where the spectral signal-to-noise ratio was above unity. Power spectral densities showed significant frequency content at $$\approx$$ ≈ 1 kHz in the shock-wave/boundary-layer interaction (SWBLI) regions. Coherence analysis showed a linear relationship between the unsteady pressures at locations underneath different SWBLI in the isolator, with the exception of the Busemann throat shock. Temporal correlation of shock positions indicated that disturbances propagated downstream at 114% of the core-flow velocity; however, improved calculations of the core-flow velocity are needed to refine this assessment. The surface pressure fields at Re = 8.5 $$\times 10^6$$ × 10 6 /m and 10.2 $$\times 10^6$$ × 10 6 /m were quantitatively very similar, and the results in the ANDLM6QT were qualitatively similar to previous studies in the Boeing/AFOSR Mach-6 Quiet Tunnel under noisy flow.

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Li, Linlin, Xu Wang, Junyi Chai, Xiaoqian Wang, Adrian Buganza-Tepole, and David M. Umulis. "Determining the role of advection in patterning by bone morphogenetic proteins through neural network model-based acceleration of a 3D finite element model of the zebrafish embryo." Frontiers in Systems Biology 2 (October 3, 2022). http://dx.doi.org/10.3389/fsysb.2022.983372.

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Embryonic development is a complex phenomenon that integrates genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogens guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes the morphogen patterns in three-dimensional (3D) space, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo, nor how the patterns are controlled over time. Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP-mediated DV patterning. The layer of epithelial cells begins to thin as they spread toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members through advection. We developed a Finite Element Model (FEM) that incorporates all stages of zebrafish embryonic development data and solves the advection-diffusion-reaction Partial Differential Equations (PDE) in a growing domain. We use the model to investigate mechanisms in underlying BMP-driven DV patterning during epiboly. Solving the PDE is computationally expensive for parameter exploration. To overcome this obstacle, we developed a Neural Network (NN) metamodel of the 3D embryo that is accurate and fast and provided a nonlinear map between high-dimensional input and output that replaces the direct numerical simulation of the PDEs. From the modeling and acceleration by the NN metamodels, we identified the impact of advection on patterning and the influence of the dynamic expression level of regulators on the BMP signaling network.

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