Lohner et al 2020b - Revision history

Cinmemj at 12:25, 20 August 2020

2020-08-20T12:25:52Z

Cinmemj: Cinmemj moved page Draft Samper 514971305 to Lohner et al 2020b

2020-07-06T11:38:55Z

Cinmemj moved page Draft Samper 514971305 to Lohner et al 2020b

Cinmemj at 11:32, 6 July 2020

2020-07-06T11:32:31Z

Cinmemj at 14:01, 1 July 2020

2020-07-01T14:01:00Z

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2020-07-01T14:00:41Z

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Cinmemj at 13:59, 1 July 2020

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← Older revision		Revision as of 12:25, 20 August 2020
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−	<!-- metadata commented in wiki content	+	Published online in ''Computational Mechanics'', 2020<br />
		+	doi: 10.1007/s00466-020-01881-7<!-- metadata commented in wiki content
	====		====

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 A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are presented, as well as appropriate numerical schemes to solve them. Several examples taken from recent evaluations of the built environment are shown, as well as the optimal placement of sensors.
-'''keywords''' Covid-19 <math>\cdot </math>Particle Methods <math>\cdot </math>Finite Elements <math>\cdot </math>           Computational Fluid Dynamics
+'''Keywords''': Covid-19, Particle Methods, Finite Elements, Computational Fluid Dynamics
 ==1 The Covid-19 Crisis==

@@ Line 137: / Line 137: @@
 An important question is then whether a particle/droplet will first reach the ground or evaporate. Figure&nbsp;2, taken from <span id='citeF-109'></span>[[#cite-109|[109]]], shows that below 120&nbsp;<math display="inline">\mu m</math> the particles evaporate before falling 2&nbsp;m (i.e. reaching the ground).
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-evap_fall_droplets.png|300px|figures/general/evap_fall_droplets.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 2&nbsp;&nbsp; Evaporation Time and Falling Time of Droplets of Varying Diameter</div>
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-evap_fall_droplets.png|500px|figures/general/evap_fall_droplets.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 2&nbsp;&nbsp; Evaporation Time and Falling Time of Droplets of Varying Diameter</div>
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">(<math>T_{p0}=33^oC, T_{\infty }=18^oC, RH=0%</math>) From <span id='citeF-109'></span>[[#cite-109|[109]]] </div>

@@ Line 23: / Line 23: @@
 An open question of great importance for all that will follow is how many viruses it takes to overwhelm the body's natural defense mechanism and trigger an infection. This number, which is sometimes called the ''viral load'' or the ''infectious dose'' will depend on numerous factors, among them the state of immune defenses of the individual, the timing of viral entry (all at once, piece by piece), and the amount of hair and mucous in the nasal vessels. In principle, a single organism in a favourable environment may replicate sufficiently to cause disease <span id='citeF-98'></span>[[#cite-98|[98]]]. Data from research performed on biological warfare agents <span id='citeF-37'></span>[[#cite-37|[37]]] suggests that both bacteria and viruses can produce disease with as few as 1-100 organisms (e.g. brucellosis 10-100, Q fever 1-10, tularaemia 10-50, smallpox 10-100, viral haemorrhagic fevers 1-10 organisms, tuberculosis 1). Compare these numbers and consider that as many as 3,000 organisms can be produced by talking for 5&nbsp;minutes or a single cough, with sneezing producing many more <span id='citeF-80'></span><span id='citeF-55'></span><span id='citeF-102'></span><span id='citeF-87'></span><span id='citeF-108'></span>[[#cite-80|[80,55,102,87,108]]]. Figure&nbsp;1, reproduced from <span id='citeF-102'></span>[[#cite-102|[102]]], shows a typical number and size distribution.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-droplet_distribution.png|600px|figures/general/droplet_distribution.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 1&nbsp;&nbsp; Counts of Particles of Various Diameters in Air Expelled by (90) Coughs <span id='citeF-80'></span>[[#cite-80|[80]]] </div>
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-droplet_distribution.png|500px|figures/general/droplet_distribution.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 1&nbsp;&nbsp; Counts of Particles of Various Diameters in Air Expelled by (90) Coughs <span id='citeF-80'></span>[[#cite-80|[80]]] </div>
 ==3 Virus Lifetime Outside the Body==

@@ Line 23: / Line 23: @@
 An open question of great importance for all that will follow is how many viruses it takes to overwhelm the body's natural defense mechanism and trigger an infection. This number, which is sometimes called the ''viral load'' or the ''infectious dose'' will depend on numerous factors, among them the state of immune defenses of the individual, the timing of viral entry (all at once, piece by piece), and the amount of hair and mucous in the nasal vessels. In principle, a single organism in a favourable environment may replicate sufficiently to cause disease <span id='citeF-98'></span>[[#cite-98|[98]]]. Data from research performed on biological warfare agents <span id='citeF-37'></span>[[#cite-37|[37]]] suggests that both bacteria and viruses can produce disease with as few as 1-100 organisms (e.g. brucellosis 10-100, Q fever 1-10, tularaemia 10-50, smallpox 10-100, viral haemorrhagic fevers 1-10 organisms, tuberculosis 1). Compare these numbers and consider that as many as 3,000 organisms can be produced by talking for 5&nbsp;minutes or a single cough, with sneezing producing many more <span id='citeF-80'></span><span id='citeF-55'></span><span id='citeF-102'></span><span id='citeF-87'></span><span id='citeF-108'></span>[[#cite-80|[80,55,102,87,108]]]. Figure&nbsp;1, reproduced from <span id='citeF-102'></span>[[#cite-102|[102]]], shows a typical number and size distribution.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-droplet_distribution.png|300px|figures/general/droplet_distribution.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 1&nbsp;&nbsp; Counts of Particles of Various Diameters in Air Expelled by (90) Coughs <span id='citeF-80'></span>[[#cite-80|[80]]] </div>
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">  [[Image:Draft_Samper_514971305-test-droplet_distribution.png|600px|figures/general/droplet_distribution.eps]]</div> <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">Figure 1&nbsp;&nbsp; Counts of Particles of Various Diameters in Air Expelled by (90) Coughs <span id='citeF-80'></span>[[#cite-80|[80]]] </div>
 ==3 Virus Lifetime Outside the Body==

← Older revision	Revision as of 11:38, 6 July 2020
(No difference)

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 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math> \svec' = - \nabla p^n + \rho {\boldsymbol g}           + \beta \rho {\boldsymbol g}(T^n - T_0) + {\boldsymbol s}_v ~~, </math>
+| style="text-align: center;" | <math> {\boldsymbol s}' = - \nabla p^n + \rho {\boldsymbol g}           + \beta \rho {\boldsymbol g}(T^n - T_0) + {\boldsymbol s}_v ~~, </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (20)
@@ Line 418: / Line 418: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math> {\boldsymbol v}^i = {\boldsymbol v}^n + \alpha ^i \gamma {\Delta t}\left(  - {\boldsymbol v}^{i-1} \cdot \nabla {\boldsymbol v}^{i-1}    \nabla \cdot \mu \nabla {\boldsymbol v}^{i-1} + \svec' \right) ~~; ~~i=1,k-1~~; </math>
+| style="text-align: center;" | <math> {\boldsymbol v}^i = {\boldsymbol v}^n + \alpha ^i \gamma {\Delta t}\left(  - {\boldsymbol v}^{i-1} \cdot \nabla {\boldsymbol v}^{i-1}    \nabla \cdot \mu \nabla {\boldsymbol v}^{i-1} + {\boldsymbol s}' \right) ~~; ~~i=1,k-1~~; </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (21a)
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 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" | <math>  \left[{ 1 \over {\Delta t}} - \theta \nabla \cdot \mu \nabla \right]    \left({\boldsymbol v}^{k} - {\boldsymbol v}^n \right)  + {\boldsymbol v}^{k-1} \cdot \nabla {\boldsymbol v}^{k-1} =    \nabla \cdot \mu \nabla {\boldsymbol v}^{k-1} + \svec' ~~.  </math>
+| style="text-align: center;" | <math>  \left[{ 1 \over {\Delta t}} - \theta \nabla \cdot \mu \nabla \right]    \left({\boldsymbol v}^{k} - {\boldsymbol v}^n \right)  + {\boldsymbol v}^{k-1} \cdot \nabla {\boldsymbol v}^{k-1} =    \nabla \cdot \mu \nabla {\boldsymbol v}^{k-1} + {\boldsymbol s}' ~~.  </math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (21b)