Albert Einstein - 2026 ACF Regionals

Question

This physicist showed the viscosity of a dilute colloidal solution is proportional to “one plus five over two phi,” where phi is the volume fraction. For 10 points each:

[10e] Name this physicist who gave the first rigorous model of Brownian motion in one of his 1905 annus mirabilis papers.

ANSWER: Albert Einstein [accept Einstein’s viscosity equation]

[10h] In Einstein’s model, this quantity of an ensemble of particles undergoing Brownian motion is proportional to the product of time and diffusion coefficient. This quantity non-linearly scales with time in anomalous diffusion.

ANSWER: mean-squared displacement [or MSD; or mean square displacement; prompt on mean squared deviation; reject partial answers]

[10m] Like any other instance of this phenomenon, the mean displacement of Brownian motion is zero. These phenomena are the random deviation of a quantity from its thermal average.

ANSWER: thermal fluctuations [or word forms like fluctuate; accept fluctuation–dissipation theorem]

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Summary


California (North)	Main Site	Y	3	16.67	100%	67%	0%
California (South)	Main Site	Y	4	12.50	100%	25%	0%
Florida	Main Site	Y	2	10.00	100%	0%	0%
Great Lakes	Main Site	Y	4	12.50	100%	25%	0%
Lower Mid-Atlantic	Main Site	Y	7	11.43	86%	14%	14%
Midwest	Main Site	Y	6	13.33	100%	33%	0%
Northeast	Main Site	Y	5	12.00	100%	20%	0%
Overflow	Main Site	Y	4	7.50	75%	0%	0%
South Central	Main Site	Y	2	10.00	100%	0%	0%
Southeast	Main Site	Y	7	15.71	100%	57%	0%
UK	Main Site	Y	6	15.00	100%	50%	0%
Upper Mid-Atlantic	Main Site	Y	7	14.29	100%	43%	0%
Upstate NY	Main Site	Y	3	13.33	100%	33%	0%

Data


Berkeley B	Berkeley A	10	0	10	20
Berkeley C	Berkeley D	10	0	0	10
Stanford B	Stanford A	10	0	10	20
UCSD B	UCLA A	10	0	0	10
UCLA B	UC Santa Barbara	10	0	10	20
UC Irvine	UCSD A	10	0	0	10
UCSD C	Arizona State	10	0	0	10
Central Florida C	Central Florida B	10	0	0	10
Florida C	Central Florida A	10	0	0	10
Pittsburgh	Michigan A	10	0	0	10
Ohio State B	Michigan C	10	0	0	10
Ohio State A	Michigan B	10	0	10	20
Ohio State C	Michigan State	10	0	0	10
James Madison B	Duke	0	0	0	0
Virginia Tech B	Liberty A	10	0	0	10
North Carolina A	Liberty B	10	0	0	10
Virginia Tech A	South Carolina B	10	0	0	10
North Carolina C	VCU	10	0	10	20
North Carolina B	Virginia	10	0	0	10
William and Mary	NC State A	10	10	0	20
Chicago B	Northwestern B	10	0	0	10
Chicago C	Illinois A	10	0	0	10
Notre Dame A	Chicago D	10	0	10	20
Chicago A	Illinois B	10	0	0	10
Indiana A	Purdue A	10	0	10	20
Illinois C	Purdue B	10	0	0	10
MIT	Bowdoin A	10	0	10	20
Harvard A	Bowdoin B	10	0	0	10
Brandeis B	Brandeis A	10	0	0	10
Brown	Southern Connecticut State	10	0	0	10
Dartmouth B	Yale	10	0	0	10
Iowa State	Carleton College	0	0	0	0
Missouri A	Claremont	10	0	0	10
Washington A	Minnesota A	10	0	0	10
Washington B	Missouri B	10	0	0	10
Texas A	Texas A&M A	10	0	0	10
Texas B	Murray State A	10	0	0	10
Tennessee A	Alabama B	10	0	10	20
Bruin	Tennessee B	10	0	0	10
Georgia Tech C	Louisville B	10	0	10	20
Georgia Tech B	Georgia Tech D	10	0	10	20
WashU B	Louisville A	10	0	0	10
Alabama A	Mississipi State	10	0	0	10
WashU A	Sewanee	10	0	10	20
Birmingham	Oxford C	10	0	0	10
Cambridge A	Southampton B	10	0	0	10
Edinburgh A	Cardiff	10	0	10	20
Montpellier	Imperial B	10	0	10	20
Southampton A	Warwick A	10	0	0	10
Manchester	Warwick B	10	0	10	20
Columbia A	Catholic	10	0	10	20
Columbia B	John Jay	10	0	0	10
Rutgers A	Johns Hopkins A	10	0	10	20
NYU A	NYU B	10	0	10	20
Maryland A	NYU C	10	0	0	10
Maryland C	Rutgers B	10	0	0	10
Georgetown	Vassar	10	0	0	10
Penn State	Binghamton B	10	0	0	10
Cornell B	Cornell C	10	0	0	10
Cornell A	Rochester	10	0	10	20