diff --git a/src/dump.cpp b/src/dump.cpp
index 8723627ec5..92ecb262d7 100644
--- a/src/dump.cpp
+++ b/src/dump.cpp
@@ -245,12 +245,21 @@ void Dump::modify_params(int narg, char **arg)
       iarg += 2;
     } else if (strcmp(arg[iarg],"every") == 0) {
       if (iarg+2 > narg) error->all("Illegal dump_modify command");
-      int n = atoi(arg[iarg+1]);
-      if (n <= 0) error->all("Illegal dump_modify command");
       int idump;
       for (idump = 0; idump < output->ndump; idump++)
 	if (strcmp(id,output->dump[idump]->id) == 0) break;
-      output->dump_every[idump] = n;
+      int n;
+      if (strstr(arg[iarg+1],"v_") == arg[iarg+1]) {
+	delete [] output->var_dump[idump];
+	n = strlen(&arg[iarg+1][2]) + 1;
+	output->var_dump[idump] = new char[n];
+	strcpy(output->var_dump[idump],&arg[iarg+1][2]);
+	n = 0;
+      } else {
+	n = atoi(arg[iarg+1]);
+	if (n <= 0) error->all("Illegal dump_modify command");
+      }
+      output->every_dump[idump] = n;
       iarg += 2;
     } else if (strcmp(arg[iarg],"first") == 0) {
       if (iarg+2 > narg) error->all("Illegal dump_modify command");
diff --git a/src/dump_dcd.cpp b/src/dump_dcd.cpp
index c8c477869a..77bf91c4dc 100644
--- a/src/dump_dcd.cpp
+++ b/src/dump_dcd.cpp
@@ -90,20 +90,17 @@ DumpDCD::~DumpDCD()
 
 void DumpDCD::init()
 {
-  // check that dump frequency has not changed
+  // check that dump frequency has not changed and is not a variable
 
-  if (nevery_save == 0) {
-    int idump;
-    for (idump = 0; idump < output->ndump; idump++)
-      if (strcmp(id,output->dump[idump]->id) == 0) break;
-    nevery_save = output->dump_every[idump];
-  } else {
-    int idump;
-    for (idump = 0; idump < output->ndump; idump++)
-      if (strcmp(id,output->dump[idump]->id) == 0) break;
-    if (nevery_save != output->dump_every[idump])
-      error->all("Cannot change dump_modify every for dump dcd");
-  }
+  int idump;
+  for (idump = 0; idump < output->ndump; idump++)
+    if (strcmp(id,output->dump[idump]->id) == 0) break;
+  if (output->every_dump[idump] == 0)
+    error->all("Cannot use variable every setting for dump dcd");
+
+  if (nevery_save == 0) nevery_save = output->every_dump[idump];
+  else if (nevery_save != output->every_dump[idump])
+    error->all("Cannot change dump_modify every for dump dcd");
 }
 
 /* ---------------------------------------------------------------------- */
diff --git a/src/output.cpp b/src/output.cpp
index b4f6b9764a..c132ab564b 100644
--- a/src/output.cpp
+++ b/src/output.cpp
@@ -18,6 +18,8 @@
 #include "style_dump.h"
 #include "atom.h"
 #include "neighbor.h"
+#include "input.h"
+#include "variable.h"
 #include "comm.h"
 #include "update.h"
 #include "group.h"
@@ -76,9 +78,11 @@ Output::Output(LAMMPS *lmp) : Pointers(lmp)
 
   ndump = 0;
   max_dump = 0;
+  every_dump = NULL;
   next_dump = NULL;
   last_dump = NULL;
-  dump_every = NULL;
+  var_dump = NULL;
+  ivar_dump = NULL;
   dump = NULL;
 
   restart = NULL;
@@ -95,9 +99,12 @@ Output::~Output()
 {
   if (thermo) delete thermo;
 
+  memory->sfree(every_dump);
   memory->sfree(next_dump);
   memory->sfree(last_dump);
-  memory->sfree(dump_every);
+  for (int i = 0; i < ndump; i++) delete [] var_dump[i];
+  memory->sfree(var_dump);
+  memory->sfree(ivar_dump);
   for (int i = 0; i < ndump; i++) delete dump[i];
   memory->sfree(dump);
 
@@ -112,6 +119,14 @@ void Output::init()
 {
   thermo->init();
   for (int i = 0; i < ndump; i++) dump[i]->init();
+  for (int i = 0; i < ndump; i++)
+    if (every_dump[i] == 0) {
+      ivar_dump[i] = input->variable->find(var_dump[i]);
+      if (ivar_dump[i] < 0)
+	error->all("Variable name for dump every does not exist");
+      if (!input->variable->equalstyle(ivar_dump[i]))
+	error->all("Variable for dump every is invalid style");
+    }
 }
 
 /* ----------------------------------------------------------------------
@@ -139,15 +154,23 @@ void Output::setup(int flag)
     for (int idump = 0; idump < ndump; idump++) {
       if (dump[idump]->clearstep) modify->clearstep_compute();
       writeflag = 0;
-      if (ntimestep % dump_every[idump] == 0 && last_dump[idump] != ntimestep)
-	writeflag = 1;
+      if (every_dump[idump] && ntimestep % every_dump[idump] == 0 && 
+	  last_dump[idump] != ntimestep) writeflag = 1;
       if (last_dump[idump] < 0 && dump[idump]->first_flag == 1) writeflag = 1;
       if (writeflag) {
 	dump[idump]->write();
 	last_dump[idump] = ntimestep;
       }
-      next_dump[idump] = 
-	(ntimestep/dump_every[idump])*dump_every[idump] + dump_every[idump];
+      if (every_dump[idump])
+	next_dump[idump] = 
+	  (ntimestep/every_dump[idump])*every_dump[idump] + every_dump[idump];
+      else {
+	int nextdump = static_cast<int> 
+	  (input->variable->compute_equal(ivar_dump[idump]));
+	if (nextdump <= ntimestep)
+	  error->all("Dump every variable returned a bad timestep");
+	next_dump[idump] = nextdump;
+      }
       if (dump[idump]->clearstep) {
 	if (writeflag) modify->addstep_compute(next_dump[idump]);
 	else modify->addstep_compute_all(next_dump[idump]);
@@ -211,7 +234,14 @@ void Output::write(int ntimestep)
         if (dump[idump]->clearstep) modify->clearstep_compute();
 	dump[idump]->write();
 	last_dump[idump] = ntimestep;
-	next_dump[idump] += dump_every[idump];
+	if (every_dump[idump]) next_dump[idump] += every_dump[idump];
+	else {
+	  int nextdump = static_cast<int> 
+	    (input->variable->compute_equal(ivar_dump[idump]));
+	  if (nextdump <= ntimestep)
+	    error->all("Dump every variable returned a bad timestep");
+	  next_dump[idump] = nextdump;
+	}
         if (dump[idump]->clearstep) modify->addstep_compute(next_dump[idump]);
       }
       if (idump) next_dump_any = MYMIN(next_dump_any,next_dump[idump]);
@@ -319,12 +349,16 @@ void Output::add_dump(int narg, char **arg)
     max_dump += DELTA;
     dump = (Dump **)
       memory->srealloc(dump,max_dump*sizeof(Dump *),"output:dump");
-    dump_every = (int *)
-      memory->srealloc(dump_every,max_dump*sizeof(int *),"output:dump_every");
+    every_dump = (int *)
+      memory->srealloc(every_dump,max_dump*sizeof(int),"output:every_dump");
     next_dump = (int *)
-      memory->srealloc(next_dump,max_dump*sizeof(int *),"output:next_dump");
+      memory->srealloc(next_dump,max_dump*sizeof(int),"output:next_dump");
     last_dump = (int *)
-      memory->srealloc(last_dump,max_dump*sizeof(int *),"output:last_dump");
+      memory->srealloc(last_dump,max_dump*sizeof(int),"output:last_dump");
+    var_dump = (char **)
+      memory->srealloc(var_dump,max_dump*sizeof(char *),"output:var_dump");
+    ivar_dump = (int *)
+      memory->srealloc(ivar_dump,max_dump*sizeof(int),"output:ivar_dump");
   }
 
   // create the Dump
@@ -339,9 +373,10 @@ void Output::add_dump(int narg, char **arg)
 
   else error->all("Invalid dump style");
 
-  dump_every[ndump] = atoi(arg[3]);
-  if (dump_every[ndump] <= 0) error->all("Illegal dump command");
+  every_dump[ndump] = atoi(arg[3]);
+  if (every_dump[ndump] <= 0) error->all("Illegal dump command");
   last_dump[ndump] = -1;
+  var_dump[ndump] = NULL;
   ndump++;
 }
 
@@ -377,14 +412,17 @@ void Output::delete_dump(char *id)
   if (idump == ndump) error->all("Could not find undump ID");
 
   delete dump[idump];
+  delete [] var_dump[idump];
 
   // move other dumps down in list one slot
 
   for (int i = idump+1; i < ndump; i++) {
     dump[i-1] = dump[i];
-    dump_every[i-1] = dump_every[i];
+    every_dump[i-1] = every_dump[i];
     next_dump[i-1] = next_dump[i];
     last_dump[i-1] = last_dump[i];
+    var_dump[i-1] = var_dump[i];
+    ivar_dump[i-1] = ivar_dump[i];
   }
   ndump--;
 }
diff --git a/src/output.h b/src/output.h
index 18db730db9..651966e812 100644
--- a/src/output.h
+++ b/src/output.h
@@ -31,8 +31,10 @@ class Output : protected Pointers {
   int max_dump;                // max size of Dump list
   int next_dump_any;           // next timestep for any Dump
   int *next_dump;              // next timestep to do each Dump
-  int *dump_every;             // output of each Dump every this many steps
+  int *every_dump;             // output of each Dump every this many steps
   int *last_dump;              // last timestep each a snapshot was output
+  char **var_dump;             // variable name for dump frequency
+  int *ivar_dump;              // variable index for dump frequency
   class Dump **dump;           // list of defined Dumps
 
   int next_restart;            // next timestep to write a restart file
diff --git a/src/variable.cpp b/src/variable.cpp
index 9fb256e259..9bd7db45cd 100644
--- a/src/variable.cpp
+++ b/src/variable.cpp
@@ -42,7 +42,8 @@ enum{ARG,OP};
 enum{DONE,ADD,SUBTRACT,MULTIPLY,DIVIDE,CARAT,UNARY,
        EQ,NE,LT,LE,GT,GE,AND,OR,
        SQRT,EXP,LN,LOG,SIN,COS,TAN,ASIN,ACOS,ATAN,
-       CEIL,FLOOR,ROUND,RAMP,VALUE,ATOMARRAY,TYPEARRAY,INTARRAY};
+       CEIL,FLOOR,ROUND,RAMP,STAGGER,LOGFREQ,
+       VALUE,ATOMARRAY,TYPEARRAY,INTARRAY};
 
 #define INVOKED_SCALAR 1
 #define INVOKED_VECTOR 2
@@ -641,7 +642,7 @@ double Variable::evaluate(char *str, Tree **tree)
         Tree *newtree = new Tree();
 	newtree->type = VALUE;
 	newtree->value = atof(number);
-	newtree->left = newtree->right = NULL;
+	newtree->left = newtree->middle = newtree->right = NULL;
 	treestack[ntreestack++] = newtree;
       } else argstack[nargstack++] = atof(number);
 
@@ -723,7 +724,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -748,7 +749,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -776,7 +777,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -838,7 +839,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	  newtree->type = ATOMARRAY;
 	  newtree->array = compute->vector_atom;
 	  newtree->nstride = 1;
-	  newtree->left = newtree->right = NULL;
+	  newtree->left = newtree->middle = newtree->right = NULL;
 	  treestack[ntreestack++] = newtree;
 
         // c_ID[i] = vector from per-atom array
@@ -864,7 +865,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	  newtree->type = ATOMARRAY;
 	  newtree->array = &compute->array_atom[0][index1-1];
 	  newtree->nstride = compute->size_peratom_cols;
-	  newtree->left = newtree->right = NULL;
+	  newtree->left = newtree->middle = newtree->right = NULL;
 	  treestack[ntreestack++] = newtree;
 
 	} else error->all("Mismatched compute in variable formula");
@@ -918,7 +919,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -936,7 +937,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -956,7 +957,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 
@@ -1002,7 +1003,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	  newtree->type = ATOMARRAY;
 	  newtree->array = fix->vector_atom;
 	  newtree->nstride = 1;
-	  newtree->left = newtree->right = NULL;
+	  newtree->left = newtree->middle = newtree->right = NULL;
 	  treestack[ntreestack++] = newtree;
 
         // f_ID[i] = vector from per-atom array
@@ -1022,7 +1023,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	  newtree->type = ATOMARRAY;
 	  newtree->array = &fix->array_atom[0][index1-1];
 	  newtree->nstride = fix->size_peratom_cols;
-	  newtree->left = newtree->right = NULL;
+	  newtree->left = newtree->middle = newtree->right = NULL;
 	  treestack[ntreestack++] = newtree;
 
 
@@ -1065,7 +1066,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = atof(var);
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = atof(var);
 
@@ -1157,7 +1158,7 @@ double Variable::evaluate(char *str, Tree **tree)
 	    Tree *newtree = new Tree();
 	    newtree->type = VALUE;
 	    newtree->value = value1;
-	    newtree->left = newtree->right = NULL;
+	    newtree->left = newtree->middle = newtree->right = NULL;
 	    treestack[ntreestack++] = newtree;
 	  } else argstack[nargstack++] = value1;
 	}
@@ -1226,9 +1227,10 @@ double Variable::evaluate(char *str, Tree **tree)
 	  newtree->type = opprevious;
 	  if (opprevious == UNARY) {
 	    newtree->left = treestack[--ntreestack];
-	    newtree->right = NULL;
+	    newtree->middle = newtree->right = NULL;
 	  } else {
 	    newtree->right = treestack[--ntreestack];
+	    newtree->middle = NULL;
 	    newtree->left = treestack[--ntreestack];
 	  }
 	  treestack[ntreestack++] = newtree;
@@ -1309,7 +1311,7 @@ double Variable::evaluate(char *str, Tree **tree)
    process an evaulation tree
    customize by adding a math function:
      sqrt(),exp(),ln(),log(),sin(),cos(),tan(),asin(),acos(),atan()
-     ceil(),floor(),round(),ramp()
+     ceil(),floor(),round(),ramp(),stagger(),logfreq()
 ---------------------------------------------------------------------- */
 
 double Variable::eval_tree(Tree *tree, int i)
@@ -1375,19 +1377,21 @@ double Variable::eval_tree(Tree *tree, int i)
 
   if (tree->type == SQRT) {
     double arg = eval_tree(tree->left,i);
-    if (arg < 0.0) error->all("Sqrt of negative in variable formula");
+    if (arg < 0.0) error->all("Sqrt of negative value in variable formula");
     return sqrt(arg);
   }
   if (tree->type == EXP)
     return exp(eval_tree(tree->left,i));
   if (tree->type == LN) {
     double arg = eval_tree(tree->left,i);
-    if (arg <= 0.0) error->all("Log of zero/negative in variable formula");
+    if (arg <= 0.0) 
+      error->all("Log of zero/negative value in variable formula");
     return log(arg);
   }
   if (tree->type == LOG) {
     double arg = eval_tree(tree->left,i);
-    if (arg <= 0.0) error->all("Log of zero/negative in variable formula");
+    if (arg <= 0.0) 
+      error->all("Log of zero/negative value in variable formula");
     return log10(arg);
   }
 
@@ -1430,6 +1434,33 @@ double Variable::eval_tree(Tree *tree, int i)
     return arg1 + delta*(arg2-arg1);
   }
 
+  if (tree->type == STAGGER) {
+    int arg1 = static_cast<int> (eval_tree(tree->left,i));
+    int arg2 = static_cast<int> (eval_tree(tree->right,i));
+    if (arg1 <= 0 || arg2 <= 0 || arg1 <= arg2)
+      error->all("Invalid math function in variable formula");
+    int lower = update->ntimestep/arg1 * arg1;
+    int delta = update->ntimestep - lower;
+    if (delta < arg2) return 1.0*(lower+arg2);
+    else return 1.0*(lower+arg1);
+  }
+
+  if (tree->type == LOGFREQ) {
+    int arg1 = static_cast<int> (eval_tree(tree->left,i));
+    int arg2 = static_cast<int> (eval_tree(tree->middle,i));
+    int arg3 = static_cast<int> (eval_tree(tree->right,i));
+    if (arg1 <= 0 || arg2 <= 0 || arg3 <= 0 || arg2 >= arg3)
+      error->all("Invalid math function in variable formula");
+    if (update->ntimestep < arg1) return 1.0*arg1;
+    else {
+      int lower = arg1;
+      while (update->ntimestep >= arg3*lower) lower *= arg3;
+      int multiple = update->ntimestep/lower;
+      if (multiple < arg2) return 1.0*(multiple+1)*lower;
+      else return 1.0*(lower*arg3);
+    }
+  }
+
   return 0.0;
 }
 
@@ -1438,6 +1469,7 @@ double Variable::eval_tree(Tree *tree, int i)
 void Variable::free_tree(Tree *tree)
 {
   if (tree->left) free_tree(tree->left);
+  if (tree->middle) free_tree(tree->middle);
   if (tree->right) free_tree(tree->right);
   delete tree;
 }
@@ -1510,7 +1542,7 @@ int Variable::int_between_brackets(char *&ptr)
    return 0 if not a match, 1 if successfully processed
    customize by adding a math function in 2 places:
      sqrt(),exp(),ln(),log(),sin(),cos(),tan(),asin(),acos(),atan()
-     ceil(),floor(),round(),ramp()
+     ceil(),floor(),round(),ramp(),stagger(),logfreq()
 ------------------------------------------------------------------------- */
 
 int Variable::math_function(char *word, char *contents, Tree **tree,
@@ -1525,7 +1557,8 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
       strcmp(word,"tan") && strcmp(word,"asin") &&
       strcmp(word,"acos") && strcmp(word,"atan") &&
       strcmp(word,"ceil") && strcmp(word,"floor") && 
-      strcmp(word,"round") && strcmp(word,"ramp"))
+      strcmp(word,"round") && strcmp(word,"ramp") &&
+      strcmp(word,"stagger") && strcmp(word,"logfreq"))
     return 0;
 
   // parse contents for arg1,arg2,arg3 separated by commas
@@ -1561,7 +1594,7 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
   // evaluate args
     
   Tree *newtree;
-  double tmp,value1,value2;
+  double tmp,value1,value2,value3;
 
   if (tree) {
     newtree = new Tree();
@@ -1569,24 +1602,37 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
     if (narg == 1) {
       tmp = evaluate(arg1,&argtree);
       newtree->left = argtree;
-      newtree->right = NULL;
+      newtree->middle = newtree->right = NULL;
     } else if (narg == 2) {
       tmp = evaluate(arg1,&argtree);
       newtree->left = argtree;
+      newtree->middle = NULL;
       tmp = evaluate(arg2,&argtree);
       newtree->right = argtree;
+    } else if (narg == 3) {
+      tmp = evaluate(arg1,&argtree);
+      newtree->left = argtree;
+      tmp = evaluate(arg2,&argtree);
+      newtree->middle = argtree;
+      tmp = evaluate(arg3,&argtree);
+      newtree->right = argtree;
     }
     treestack[ntreestack++] = newtree;
   } else {
-    if (narg == 1)
+    if (narg == 1) {
       value1 = evaluate(arg1,NULL);
-    else if (narg == 2) {
+    } else if (narg == 2) {
       value1 = evaluate(arg1,NULL);
       value2 = evaluate(arg2,NULL);
+    } else if (narg == 3) {
+      value1 = evaluate(arg1,NULL);
+      value2 = evaluate(arg2,NULL);
+      value3 = evaluate(arg3,NULL);
     }
   }
     
   if (strcmp(word,"sqrt") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = SQRT;
     else {
       if (value1 < 0.0) 
@@ -1595,9 +1641,11 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
     }
 
   } else if (strcmp(word,"exp") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = EXP;
     else argstack[nargstack++] = exp(value1);
   } else if (strcmp(word,"ln") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = LN;
     else {
       if (value1 <= 0.0) 
@@ -1605,6 +1653,7 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
       argstack[nargstack++] = log(value1);
     }
   } else if (strcmp(word,"log") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = LOG;
     else {
       if (value1 <= 0.0) 
@@ -1613,16 +1662,20 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
     }
 
   } else if (strcmp(word,"sin") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = SIN;
     else argstack[nargstack++] = sin(value1);
   } else if (strcmp(word,"cos") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = COS;
     else argstack[nargstack++] = cos(value1);
   } else if (strcmp(word,"tan") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = TAN;
     else argstack[nargstack++] = tan(value1);
 
   } else if (strcmp(word,"asin") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = ASIN;
     else {
       if (value1 < -1.0 || value1 > 1.0) 
@@ -1630,6 +1683,7 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
       argstack[nargstack++] = asin(value1);
     }
   } else if (strcmp(word,"acos") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = ACOS;
     else {
       if (value1 < -1.0 || value1 > 1.0) 
@@ -1637,22 +1691,27 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
       argstack[nargstack++] = acos(value1);
     }
   } else if (strcmp(word,"atan") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = ATAN;
     else argstack[nargstack++] = atan(value1);
 
   } else if (strcmp(word,"ceil") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = CEIL;
     else argstack[nargstack++] = ceil(value1);
 
   } else if (strcmp(word,"floor") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = FLOOR;
     else argstack[nargstack++] = floor(value1);
 
   } else if (strcmp(word,"round") == 0) {
+    if (narg != 1) error->all("Invalid math function in variable formula");
     if (tree) newtree->type = ROUND;
     else argstack[nargstack++] = MYROUND(value1);
 
   } else if (strcmp(word,"ramp") == 0) {
+    if (narg != 2) error->all("Invalid math function in variable formula");
     if (update->whichflag == 0)
       error->all("Cannot use ramp in variable formula between runs");
     if (tree) newtree->type = RAMP;
@@ -1661,6 +1720,39 @@ int Variable::math_function(char *word, char *contents, Tree **tree,
       delta /= update->endstep - update->beginstep;
       argstack[nargstack++] = value1 + delta*(value2-value1);
     }
+
+  } else if (strcmp(word,"stagger") == 0) {
+    if (narg != 2) error->all("Invalid math function in variable formula");
+    if (tree) newtree->type = STAGGER;
+    else {
+      int ivalue1 = static_cast<int> (value1);
+      int ivalue2 = static_cast<int> (value2);
+      if (ivalue1 <= 0 || ivalue2 <= 0 || ivalue1 <= ivalue2)
+	error->all("Invalid math function in variable formula");
+      int lower = update->ntimestep/ivalue1 * ivalue1;
+      int delta = update->ntimestep - lower;
+      if (delta < value2) argstack[nargstack++] = lower+ivalue2;
+      else argstack[nargstack++] = lower+ivalue1;
+    }
+
+  } else if (strcmp(word,"logfreq") == 0) {
+    if (narg != 3) error->all("Invalid math function in variable formula");
+    if (tree) newtree->type = LOGFREQ;
+    else {
+      int ivalue1 = static_cast<int> (value1);
+      int ivalue2 = static_cast<int> (value2);
+      int ivalue3 = static_cast<int> (value3);
+      if (ivalue1 <= 0 || ivalue2 <= 0 || ivalue3 <= 0 || ivalue2 >= ivalue3)
+	error->all("Invalid math function in variable formula");
+      if (update->ntimestep < ivalue1) argstack[nargstack++] = ivalue1;
+      else {
+	int lower = ivalue1;
+	while (update->ntimestep >= ivalue3*lower) lower *= ivalue3;
+	int multiple = update->ntimestep/lower;
+	if (multiple < ivalue2) argstack[nargstack++] = (multiple+1)*lower;
+	else argstack[nargstack++] = lower*ivalue3;
+      }
+    }
   }
 
   delete [] arg1;
@@ -1898,7 +1990,7 @@ int Variable::group_function(char *word, char *contents, Tree **tree,
     Tree *newtree = new Tree();
     newtree->type = VALUE;
     newtree->value = value;
-    newtree->left = newtree->right = NULL;
+    newtree->left = newtree->middle = newtree->right = NULL;
     treestack[ntreestack++] = newtree;
   } else argstack[nargstack++] = value;
 
@@ -1966,7 +2058,7 @@ void Variable::peratom2global(int flag, char *word,
     Tree *newtree = new Tree();
     newtree->type = VALUE;
     newtree->value = value;
-    newtree->left = newtree->right = NULL;
+    newtree->left = newtree->middle = newtree->right = NULL;
     treestack[ntreestack++] = newtree;
   } else argstack[nargstack++] = value;
 }
@@ -2009,7 +2101,7 @@ void Variable::atom_vector(char *word, Tree **tree,
   Tree *newtree = new Tree();
   newtree->type = ATOMARRAY;
   newtree->nstride = 3;
-  newtree->left = newtree->right = NULL;
+  newtree->left = newtree->middle = newtree->right = NULL;
   treestack[ntreestack++] = newtree;
 	    
   if (strcmp(word,"mass") == 0) {
diff --git a/src/variable.h b/src/variable.h
index 5b344b708a..75279348c1 100644
--- a/src/variable.h
+++ b/src/variable.h
@@ -50,7 +50,7 @@ class Variable : protected Pointers {
     int *iarray;
     int nstride;
     int type;
-    Tree *left,*right;
+    Tree *left,*middle,*right;
   };
 
   void remove(int);