Existence of spiky steady state of chemotaxis models with logarithm sensitivity

2020 ◽  
Vol 44 (2) ◽  
pp. 1484-1499
Author(s):  
Xin Xu
Keyword(s):  
Steady State ◽  
Chemotaxis Models

scholarly journals Pattern Formation in Keller–Segel Chemotaxis Models with Logistic Growth

2016 ◽  
Vol 26 (02) ◽  
pp. 1650033 ◽  
Author(s):  
Ling Jin ◽  
Qi Wang ◽  
Zengyan Zhang
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Neumann Boundary ◽  
Steady States ◽  
Local Theory ◽  
Logistic Growth ◽  
Homogeneous Steady State ◽  
Cellular Aggregation ◽  
Chemotaxis Models ◽  
Steady State Stability

In this paper, we investigate pattern formation in Keller–Segel chemotaxis models over a multidimensional bounded domain subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as chemoattraction rate [Formula: see text] increases. Then using Crandall–Rabinowitz local theory with [Formula: see text] being the bifurcation parameter, we obtain the existence of nonhomogeneous steady states of the system which bifurcate from this homogeneous steady state. Stability of the bifurcating solutions is also established through rigorous and detailed calculations. Our results provide a selection mechanism of stable wavemode which states that the only stable bifurcation branch must have a wavemode number that minimizes the bifurcation value. Finally, we perform extensive numerical simulations on the formation of stable steady states with striking structures such as boundary spikes, interior spikes, stripes, etc. These nontrivial patterns can model cellular aggregation that develop through chemotactic movements in biological systems.

Studies on Water in the Hydration Chamber of a Modified Electron Microscope

1970 ◽  
Vol 28 ◽  
pp. 544-545
Author(s):  
R. C. Moretz ◽  
G. G. Hausner ◽  
D. F. Parsons
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Electron Microscope ◽  
Steady State ◽  
Room Temperature ◽  
Small Mass ◽  
Equilibrium Pressure ◽  
Biological Objects ◽  
Mechanical Pump ◽  
Differential Pumping

Use of the electron microscope to examine wet objects is possible due to the small mass thickness of the equilibrium pressure of water vapor at room temperature. Previous attempts to examine hydrated biological objects and water itself used a chamber consisting of two small apertures sealed by two thin films. Extensive work in our laboratory showed that such films have an 80% failure rate when wet. Using the principle of differential pumping of the microscope column, we can use open apertures in place of thin film windows.Fig. 1 shows the modified Siemens la specimen chamber with the connections to the water supply and the auxiliary pumping station. A mechanical pump is connected to the vapor supply via a 100μ aperture to maintain steady-state conditions.

Continuous hydrogenolysis of acetal-stabilized lignin in flow

2021 ◽  
Author(s):  
Wu Lan ◽  
Yuan Peng Du ◽  
Songlan Sun ◽  
Jean Behaghel de Bueren ◽  
Florent Héroguel ◽  
...  
Keyword(s):  
Steady State ◽  
Challenges And Opportunities

We performed a steady state high-yielding depolymerization of soluble acetal-stabilized lignin in flow, which offered a window into challenges and opportunities that will be faced when continuously processing this feedstock.

Network reconstruction based on steady-state data

2008 ◽  
Vol 45 ◽  
pp. 161-176 ◽  
Author(s):  
Eduardo D. Sontag
Keyword(s):  
Steady State ◽  
Reverse Engineering ◽  
Theoretical Method ◽  
Network Reconstruction ◽  
Quasi Steady State ◽  
State Data

This paper discusses a theoretical method for the “reverse engineering” of networks based solely on steady-state (and quasi-steady-state) data.

Steady State Disinfection of Water By Ozone and sonozone

1979 ◽  
Vol 1 (4) ◽  
pp. 13-24
Author(s):  
E. Dahi ◽  
E. Lund
Keyword(s):  
Steady State

Olfactory Modulation of Steady- State Visual Evoked Potential Topography in Comparison with Differences in Odor Sensitivity

2002 ◽  
Vol 16 (2) ◽  
pp. 71-81 ◽  
Author(s):  
Caroline M. Owen ◽  
John Patterson ◽  
Richard B. Silberstein
Keyword(s):  
Steady State ◽  
Visual Evoked Potential ◽  
Evoked Potential ◽  
Behavioral Responses ◽  
Simultaneous Recording ◽  
Odor Concentration ◽  
Odor Detection ◽  
Detection Response ◽  
Response Groups ◽  
Visual Evoked

Summary Research was undertaken to determine whether olfactory stimulation can alter steady-state visual evoked potential (SSVEP) topography. Odor-air and air-only stimuli were used to determine whether the SSVEP would be altered when odor was present. Comparisons were also made of the topographic activation associated with air and odor stimulation, with the view toward determining whether the revealed topographic activity would differentiate levels of olfactory sensitivity by clearly identifying supra- and subthreshold odor responses. Using a continuous respiration olfactometer (CRO) to precisely deliver an odor or air stimulus synchronously with the natural respiration, air or odor (n-butanol) was randomly delivered into the inspiratory airstream during the simultaneous recording of SSVEPs and subjective behavioral responses. Subjects were placed in groups based on subjective odor detection response: “yes” and “no” detection groups. In comparison to air, SSVEP topography revealed cortical changes in response to odor stimulation for both response groups, with topographic changes evident for those unable to perceive the odor, showing the presence of a subconscious physiological odor detection response. Differences in regional SSVEP topography were shown for those who reported smelling the odor compared with those who remained unaware of the odor. These changes revealed olfactory modulation of SSVEP topography related to odor awareness and sensitivity and therefore odor concentration relative to thresholds.

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