Improve numerical stability of exchange current density and OCPs

[MarcBerliner]

Description

Exchange current densities include sqrt(c_e), sqrt(c_s), and sqrt(c_max - c_s) terms that blow up when concentrations -> 0/c_max. Inverse BV kinetics do arcsinh(j/j0), which also blows up when j0 is small or causes divide by zero errors for j0=0. These cause solver failures in edge cases

This PR adds regularised versions of two expressions:

• RegPower(x, a): approximates |x|^a * sign(x) but stays linear near zero (based on modelica's regPow)
• Arcsinh2(a, b): computes arcsinh(a/b) while avoiding blowup/division by zero errors as b -> 0

Major changes:

• The exchange current density now automatically replaces all Sqrt/Power -> RegPower to make them more numerically stable at small concentrations
• The barrier function for the OCP is changed from 1e-6/sto to a more complicated logarithmic expression, whose parameters were tuned to provide a barrier of 1 mV at sto = 0.001 and 1000 mV at sto = 0. This is a significant from the previous version because we no longer have an asymptote as sto -> 0. Some calculations that relied on this assumption, like the ESOH solver, will have slightly different answers in this extreme limit. Most usecases will not change

Type of change

Please add a line in the relevant section of CHANGELOG.md to document the change (include PR #)

Important checks:

Please confirm the following before marking the PR as ready for review:

• No style issues: nox -s pre-commit
• All tests pass: nox -s tests
• The documentation builds: nox -s doctests
• Code is commented for hard-to-understand areas
• Tests added that prove fix is effective or that feature works

[codecov]

Codecov Report

❌ Patch coverage is 91.76030% with 22 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.32%. Comparing base (c18ea21) to head (66a0155).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/pybamm/expression_tree/functions.py	86.04%	18 Missing ⚠️
src/pybamm/expression_tree/binary_operators.py	90.90%	2 Missing ⚠️
...rc/pybamm/expression_tree/operations/regularise.py	98.30%	1 Missing ⚠️
...nterface/kinetics/inverse_kinetics/base_inverse.py	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5371      +/-   ##
==========================================
+ Coverage   98.03%   98.32%   +0.28%     
==========================================
  Files         327      328       +1     
  Lines       28690    28941     +251     
==========================================
+ Hits        28126    28455     +329     
+ Misses        564      486      -78     

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[BradyPlanden]

Thanks @MarcBerliner - this is looking good. Just a few questions / comments

[BradyPlanden]

Looks great, thanks @MarcBerliner! Just one non-blocking comment