In line with the first law of thermodynamics, Bernoulli's principle states that the total energy in a fluid is the same at all points. We applied Bernoulli's principle to understand the relationship between intracranial pressure (ICP) and intracranial fluids. We analyzed simple fluid physics along a tube to describe the interplay between pressure and velocity. Bernoulli's equation demonstrates that a fluid does not flow along a gradient of pressure or velocity; a fluid flows along a gradient of energy from a high-energy region to a low-energy region. A fluid can even flow against a pressure gradient or a velocity gradient. Pressure and velocity represent part of the total energy. Cerebral blood perfusion is not driven by pressure but by energy: the blood flows from high-energy to lower-energy regions. Hydrocephalus is related to increased cerebrospinal fluid (CSF) resistance (i.e., energy transfer) at various points. Identification of the energy transfer within the CSF circuit is important in understanding and treating CSF-related disorders. Bernoulli's principle is not an abstract concept far from clinical practice. We should be aware that pressure is easy to measure, but it does not induce resumption of fluid flow. Even at the bedside, energy is the key to understanding ICP and fluid dynamics.
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http://dx.doi.org/10.1007/978-3-319-22533-3_21 | DOI Listing |
Sci Rep
December 2024
School of Civil Engineering and Architecture, University of Jinan, Jinan, 250022, China.
In this paper, the free vibration of piezoelectric nanobeams considering static flexoelectric, dynamic flexoelectric, and surface effects is studied. Based on the theories of the Timoshenko beam and Euler-Bernoulli beam, a theoretical model of flexoelectric nanobeams is established and the governing equations and boundary conditions of this model are derived using the variational principle. Then, the analytical solution of the frequency equation is obtained by using the Navier method.
View Article and Find Full Text PDFRev Sci Instrum
December 2024
School of Mechanical Engineering, Northeast Electric Power University, Jilin 132012, China.
This work proposes a new rotary piezoelectric energy harvester using magnetic excitation inspired by the fan blade. The configuration and operating principle of the harvester are introduced. Then, the equivalent nonlinear model of the piezoelectric beam is established based on the Euler-Bernoulli theory and the Rayleigh-Ritz method.
View Article and Find Full Text PDFSpiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation for neural dynamics, there exists numerous software and hardware solutions and stacks whose variability makes it difficult to reproduce findings. Here, we establish a common reference frame for computations in digital neuromorphic systems, titled Neuromorphic Intermediate Representation (NIR).
View Article and Find Full Text PDFSensors (Basel)
August 2024
Pulmonology Department, Santa Maria Local Health Unit, 1769-001 Lisbon, Portugal.
The high cost and limited availability of home spirometers pose a significant barrier to effective respiratory disease management and monitoring. To address this challenge, this paper introduces a novel Venturi-based spirometer designed for home use, leveraging the Bernoulli principle. The device features a 3D-printed Venturi tube that narrows to create a pressure differential, which is measured by a differential pressure sensor and converted into airflow rate.
View Article and Find Full Text PDFArch Ration Mech Anal
May 2024
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, 5, 56127 Pisa, Italy.
We prove the first regularity theorem for the free boundary of solutions to shape optimization problems involving integral functionals, for which the energy of a domain is obtained as the integral of a cost function (, ) depending on the solution of a certain PDE problem on . The main feature of these functionals is that the minimality of a domain cannot be translated into a variational problem for a single (real or vector valued) state function. In this paper we focus on the case of affine cost functions , where is the solution of the PDE with Dirichlet boundary conditions.
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