(no subject)



Hi all.

At the end of this message is a batch file defining and attenpting to solve
a system of two non-linear equations.  Also included is the result of
attempting to run that batch file on Windows Maxima 5.9.1.

Am I being overly optimistic in hoping that Maxima would solve those
equations or is this a bug, (perhaps GCL/Windows specific)?

Note that the variable eq1 has it's name altered to EQ1 at input.

=========================================================

%i26) 			       DISPLAY2D : FALSE
(%o26) FALSE
(%i27) K_1:37
(%o27) 37
(%i28) mu_1:44
(%o28) 44
(%i29) alpha_1:1
(%o29) 1
(%i30) x_1:0.7
(%o30) 0.7
(%i31) K_2:2.25
(%o31) 2.25
(%i32) mu_2:0
(%o32) 0
(%i33) alpha_2:1
(%o33) 1
(%i34) x_2:0.29
(%o34) 0.29
(%i35) K_3:2.25
(%o35) 2.25
(%i36) mu_3:0
(%o36) 0
(%i37) alpha_3:0.01
(%o37) 0.01
(%i38) x_3:0.01
(%o38) 0.01
(%i39) beta_sc:mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)
(%o39) mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)
(%i40) zeta_sc:mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))
(%o40) mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))
(%i41) P1:(4*mu_sc/3+K_sc)/(4*mu_sc/3+K_1)
(%o41) (4*mu_sc/3+K_sc)/(4*mu_sc/3+37)
(%i42) Q1:(zeta_sc+mu_sc)/(zeta_sc+mu_1)
(%o42) (mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+mu_sc)
	/(mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+44)
(%i43) P2:(4*mu_sc/3+K_sc)/(4*mu_sc/3+K_2)
(%o43) (4*mu_sc/3+K_sc)/(4*mu_sc/3+2.25)
(%i44) Q2:(zeta_sc+mu_sc)/(zeta_sc+mu_2)
(%o44) 6*(2*mu_sc+K_sc)*(mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+mu_sc)
	/(mu_sc*(8*mu_sc+9*K_sc))
(%i45) P3:(4*mu_3/3+K_sc)/(%PI*alpha_3*beta_sc+4*mu_3/3+K_3)
(%o45) K_sc/(0.01*%PI*mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)+2.25)
(%i46) Q3:(2*(2*(mu_sc+mu_3)/3+K_3)/(%PI*alpha_3*beta_sc+4*mu_3/3+K_3)
	  +8*mu_sc/(%PI*alpha_3*(2*beta_sc+mu_sc)+4*mu_3)+1)
	  /5
(%o46) (2*(2*mu_sc/3+2.25)/(0.01*%PI*mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)
			   +2.25)
	+800.0*mu_sc/(%PI*(2*mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)+mu_sc))+1)
	/5
(%i47) EQ1:x_3*(K_3-K_sc)*P3+x_2*(K_2-K_sc)*P2+x_1*(K_1-K_sc)*P1 = 0
(%o47) 0.01*(2.25-K_sc)*K_sc/(0.01*%PI*mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)
			     +2.25)
	+0.7*(37-K_sc)*(4*mu_sc/3+K_sc)/(4*mu_sc/3+37)
	+0.29*(2.25-K_sc)*(4*mu_sc/3+K_sc)/(4*mu_sc/3+2.25)
	 = 0
(%i48) eq2:x_3*(mu_3-mu_sc)*Q3+x_2*(mu_2-mu_sc)*Q2+x_1*(mu_1-mu_sc)*Q1 = 0
(%o48) -0.002*mu_sc
	     *(2*(2*mu_sc/3+2.25)/(0.01*%PI*mu_sc*(mu_sc+3*K_sc)
				  /(4*mu_sc+3*K_sc)
				  +2.25)
	      +800.0*mu_sc/(%PI*(2*mu_sc*(mu_sc+3*K_sc)/(4*mu_sc+3*K_sc)
				+mu_sc))+1)
	+0.7*(44-mu_sc)*(mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+mu_sc)
	 /(mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+44)
	-1.74*(2*mu_sc+K_sc)*(mu_sc*(8*mu_sc+9*K_sc)/(6*(2*mu_sc+K_sc))+mu_sc)
	 /(8*mu_sc+9*K_sc)
	 = 0
(%i49) ALGSYS([EQ1,eq2],[K_sc,mu_sc])
Maxima encountered a Lisp error:

 Error in CATCH [or a callee]: Bind stack overflow.

Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
=========================================================


Cheers

Mike Thomas.




=========================================================

/* display2d: false; */

/*
 * Constants
 */


/* spherical quartz grains */

K_1: 37;  /* GPa */
mu_1: 44; /* GPa */
alpha_1: 1;
x_1: 0.7;


/* spherical pores filled with water */

K_2: 2.25;  /* GPa */
mu_2: 0; /* GPa */
alpha_2: 1;
x_2: 0.29;


/* thin penny shaped cracks filled with water */

K_3: 2.25;  /* GPa */
mu_3: 0; /* GPa */
alpha_3: 0.01;
x_3: 0.01;



/*
 * Shape coefficients
 */

beta_sc: mu_sc * ( 3 * K_sc + mu_sc ) / ( 3 * K_sc + 4 * mu_sc );
zeta_sc: mu_sc * ( 9 * K_sc + 8 * mu_sc ) / ( 6 * ( K_sc + 2 * mu_sc ) );

P1: (K_sc + 4/3 * mu_sc) / (K_1 + 4/3 * mu_sc);
Q1: (mu_sc + zeta_sc) / (mu_1 + zeta_sc);

P2: (K_sc + 4/3 * mu_sc) / (K_2 + 4/3 * mu_sc);
Q2: (mu_sc + zeta_sc) / (mu_2 + zeta_sc);

P3: (K_sc + 4/3 * mu_3) / (K_3 + 4/3 * mu_3 + %pi * alpha_3 * beta_sc);
Q3: 1/5 * (1 + (8 * mu_sc / (4 * mu_3 + %pi * alpha_3 * (mu_sc + 2 *
beta_sc)))
  + 2 * ((K_3 + 2/3 * (mu_3 + mu_sc)) / (K_3 + 4/3 * mu_3 + %pi * alpha_3 *
beta_sc)));


/* Coupled Equations */

eq1: x_1 * (K_1 - K_sc) * P1 + x_2 * (K_2 - K_sc) * P2 + x_3 * (K_3 - K_sc)
* P3 = 0;
eq2: x_1 * (mu_1 - mu_sc) * Q1 + x_2 * (mu_2 - mu_sc) * Q2 + x_3 * (mu_3 -
mu_sc) * Q3 = 0;

/* Solve the two equations */

algsys( [eq1, eq2], [K_sc, mu_sc] );