No class Mon 11/7 (ISCB conference)
HW7 due Fri 10/28
quiz MR + Ch 10 Fri 10/28
Boltzmann + F=-kTlnQ
Also no class Fri 11/18 (Thanksgiving)
Exam II Fri 11/11
In a two-particle system, energies of the
Regular solution model:
HW 11 due 12/9
Fmix
= AB x(1 x) + x ln x + (1 x) ln(1 x)
NkT
U mix
can be + or -mole fractions:
x = xA = N A N
1 x = xB = N B N
U mix from lattice model and energy of
AB contac
Beer Office Hrs: Fri 9/30 10am, Mon 10/3 10am Clark 316
No class Wed 10/5 (MB at NIH)
Exam I Thru Ch 5 Entropy & the Boltzmann Law
Friday Oct 7 in class, 11-11:50am. Calculators & 1pg. notes
Will post
HW1 due Fri 9/9 Read Ch 1, 2, and 3
Why probability? We have no hope of fully describing the precise state of a macro-molecular
system. The beauty and power of stat mech is that probabilistic approach
HW9 due 11/25
S = Nk ln
3
2
cU V
N
Ideal Gas
2-state system
5
2
3
Nk ln U
2
cV
+ Nk ln 5 / 2
N
S (U ) =
1 S
3 Nk
=
=
T U V , N 2 U
T=
2
U
3 Nk
f excited
1
k
= ln
T
0 f ground
=
k
0
ln
U
N 0 U
Ideal
Exam II Fri 11/11 will cover Ch6 - Ch 11:
Exam II Practice Problems posted
Review Session next week
HW9 will be due in 2 weeks
2 2
2
2
2 + 2 + 2 + V ( x, y, z ) = j
i
=
z
t
2m x y
+ V ( x, y, z
580.321 Statistical Mechanics and Thermodynamics
Fall 2016
Course Description:
This course will introduce the basic principles of statistical physics and thermodynamics as
they apply to biological sys
Statistical Mechanics:
Ch 6,7 HW5 due 10/14
Thermodynamic systems in maximum entropy state subject to constraints on (U,V,N).
When constraints are released (energy flows, etc) new equilibrium is max
HW 3 due Fri
Generalization of Lagrange multiplier technique to functions of t variables: f ( x1 , x2 , , xt )
extrema of
f ( x1 , x2 , , xt ) subject to constraint g ( x1 , x2 , , xt ) = c
t
g
f
dg =
Chapter 1
Principles of Probability
1. Combining independent probabilities.
You have applied to three medical schools: University of California at San Francisco (UCSF),
Duluth School of Mines (DSM), a
Quiz 3 Fri (Ch 4)
There is an extensive function S = k ln W
, and we call this quantity the entropy
Because lnW is monotonic, maximizing S maximizes W.
The entropy can also be written in terms of the
Ch 4 Multivariate calculus:
multivariate functions assign one value to y for each set
of values (x1, x2,xt): y=f(x1, x2,xt)
Partial derivatives:
f ( x + x, y ) f ( x, y )
f
= lim
x
x y x0
f
f (
HW6 posted due Fri 10/21
Quiz Ch8 Thurs 10/20
From fundamental equations:
dU = TdS pdV + dN
p
1
dS = dU + dV dN
T
T
T
dF = SdT pdV + dN
dH = TdS + Vdp + dN
dG = SdT + Vdp + dN
for const Volume and dN=
Exam: Fri 10/7/2016 Maryland 110 11-11:50am
Review Mon 7-9pm, Exam I practice posted
will post practice answers Tues night
Topics: (thru Ch 5)
8.5x11 sheet, CALCULATOR
Basic Probability and Combinator
Maxwells Relations.
Fundamental Equations:
dU = TdS pdV + dN
dF = SdT pdV + dN
dH = TdS + Vdp + dN
dG = SdT + Vdp + dN
Quiz Thurs, HW6 due Fri
U ( S ,V , N )
F (T , V , N ) = U TS
H ( S , p, N ) = U +
Appendix A,C (2nd Ed): Series & Approximations
HW2 due Fri 9/16
n
sn = ax k 1 = a + ax + ax 2 + + ax n 1
geometric series:
k =1
sn x = ax + ax 2 + ax 3 + + ax n
sn sn x = a ax
The infinite series:
s =
When the total energy, or average energy per particle, is constrained, maximizing S leads to
exponential distributions:
t
t
st
1 constraint: g ( p1 , p2 , pt ) = pi = 1
S = p ln p
i =1
i =1
t
E
constr
Ch 15. Solutions and mixtures:
HW10 due 12/2, HW11 due 12/9
Quiz Fri 12/2 Ch13,14
The entropy change of mixing NA molecules of type A, and NB molecules of type B is:
S mix = k ln W = k ln
N!
N A! N B
Exam II Fri 11/11 Ch 6-11
HW9 will be due in 2 weeks
Topics:
Fundamental Eqn for Energy U(S,V,N), defs of T,p,
Defs and Fund Eqns for S(U,V,N) ,F(T,V,N),H(S,p,N),G(T,p,N) and others
Lattice Model of I
Read Ch 10. The Boltzmann Distribution Law
t
E and
Before, with fixed:
= i pi =
i =1
maximized when
e i
*
pi =
q
t
q = e
N
t
p
i =1
i
HW 7 due 10/28
t
S = k pi ln pi
=1
i =1
determined by :
i
t
t
i
Exam: Fri 10/7/2016 Maryland 110 11:00-11:50am
Review Session
HW5 due in ~2 weeks
Topics: (thru Ch 5)
8.5x11 sheet, will post practice problems Thurs night
Basic Probability and Combinatorics
t
Probab
Read Ch 2. Extremum Principles
HW2 posted, due 9/16 also read Ch. 3
The state of a system is specified by the positions x i and velocities v i of its components.
The dynamics of system specified by Ne
Homework #1 Systems Bioengineering I, Fall 2011, page 1 of 7
Homework 1: Ion-channel permeation
(100 points in total)
1. (20 pts) Consider the dimensionally pseudo-realistic permeation pathway shown i
Homework XX - Contractile Mechanisms I and II
65 points total = 10 + 31 + 24
1) (10 points total, 1 point each) MUSCLE SECTION, SLIDING FILAMENT THEORY. Use
the following graph for maximally activated
Homework - Contractile Mechanisms Part II: Huxley 57 Derivation and Simulation,
Types of Muscle, and Excel-based Monte Carlo Simulation
Total points:90 = 10 + 35 + 30 + 15
1) (10 points) HUXLEY 57 MOD
Homework 5 Excel-based Huxley 57 Simulation, Types of Muscle, and Excelbased Monte Carlo Simulation
Four problems for 90 points total = 29 + 30 + 20 + 11
1) (Please use the 2008 Excel-based implementa
Homework #2 KEY for Yue section of Systems Bioengineering I, Fall 2011, page 1 of 9
Homework 2 KEY: Ion-channel gating (100 points in total)
1. (40 pts) Consider a simple human voltage-activated K cha
Homework XX - Contractile Mechanisms I and II
65 points total = 10 + 31 + 24
1) (10 points total, 1 point each) MUSCLE SECTION, SLIDING FILAMENT THEORY. Use
the following graph for maximally activated
Homework #1 for Yue section of SBE I, Fall 2009, page 1 of 9
Homework 1: Ion-channel permeation
(100 points in total)
1. (10 pts) Consider the network of BR-permeation channels, placed in series as dr