[ase-users] trajectory format error during structure optimization

Aldo Ugolotti aldo.ugolotti at unimib.it
Wed Jul 10 08:44:22 CEST 2024


Dear Adam,

you are right, I was mistaking the scope of the "traj" argument in the 
optimizer. Now everything works as expected.

Thank you very much for the support.

Aldo

On 7/8/24 18:07, Adam Jackson wrote:
>
> If using filters, you need to attach the trajectory to the Atoms 
> rather than the filter class. See 
> https://wiki.fysik.dtu.dk/ase/ase/filters.html#the-unitcellfilter-class
>
> That seems like an easy mistake to make because the optimizer provides 
> a “traj” argument. Perhaps this bit of user experience can be improved…
>
> Happy calculating,
>
> Adam
>
> *From: *Aldo Ugolotti <aldo.ugolotti at unimib.it>
> *Date: *Monday, 8 July 2024 at 16:24
> *To: *Adam Jackson <a.j.jackson at physics.org>, 
> ase-users at listserv.fysik.dtu.dk <ase-users at listserv.fysik.dtu.dk>, 
> David Willock <WillockDJ at cardiff.ac.uk>
> *Subject: *Re: trajectory format error during structure optimization
>
> Dear Adam,
>
> yes I am using a filter to optimize the cell under an anisotropic 
> stress, i.e. using TS-ASE module.
>
> Here is a snapshot of the script I am using to do it:
>
> from ase.optimize.fire import FIRE
> from ase import *
> from ase.io import read,write
> import os
> import sys
> import numpy as np
> from tsase.mushybox import mushybox
> from ase.calculators.vasp import Vasp
>
> p1 = read('POSCAR',format='vasp')
>
> calc = Vasp(xc   = 'pbesol',
>             ediff = 1.0e-6,
>             kpts = (1,1,1),
>             gamma= True
>               )
> p1.set_calculator(calc)
>
> stress=np.zeros((3,3))
> stress[0][0] = 01.0 ## units: in GPa
> stress[1][1] = 01.0
> stress[2][2] = 00.0
>
> p1box = mushybox(p1,express=stress)
> dyn = FIRE(p1box,maxstep = 0.1, trajectory='opt.traj', dt = 0.01, 
> dtmax = 0.1, force_consistent = False)
> dyn.run(fmax=0.005, steps=1000)
> write("CONTCARfin",p1,format='vasp')
>
> Actually, I assumed that the writing part was included within the base 
> class of the optimizator, I tried to verify it by looking directly in 
> the code, but I am not so experienced with ASE modules to fully trace 
> the trajectory writing routine.
>
> To reply also to David Willock, no, the trajectory file seems not 
> empty; I am attaching a copy of it to try and open it up.
>
> Thanks,
>
> Aldo
>
> On 08/07/2024 15:54, Adam Jackson wrote:
>
>     Hmm, there are 20 atoms in the structure but 23 positions in the
>     trajectory information… I wonder if this is something to do with
>     using a filter on the optimiser that exposes some extra degrees of
>     freedom. I would expect that to add more than 3 values, though.
>     Maybe some were removed with constraints?
>
>     Can you show us the code that created the optimiser/trajectory? Or
>     make a small reproducible example using the EMT calculator?
>
>     Cheers,
>
>     Adam
>
>     *From: *ase-users <ase-users-bounces at listserv.fysik.dtu.dk>
>     <mailto:ase-users-bounces at listserv.fysik.dtu.dk> on behalf of
>     ase-users-request at listserv.fysik.dtu.dk
>     <ase-users-request at listserv.fysik.dtu.dk>
>     <mailto:ase-users-request at listserv.fysik.dtu.dk>
>     *Date: *Monday, 8 July 2024 at 14:37
>     *To: *ase-users at listserv.fysik.dtu.dk
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     *Subject: *ase-users Digest, Vol 193, Issue 2
>
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>     Today's Topics:
>
>        1. Re: trajectory format error during structure optimization
>           (Aldo Ugolotti)
>        2. Re: trajectory format error during structure optimization
>           (David Willock)
>
>
>     ----------------------------------------------------------------------
>
>     Message: 1
>     Date: Mon, 8 Jul 2024 14:40:08 +0200
>     From: Aldo Ugolotti <aldo.ugolotti at unimib.it>
>     <mailto:aldo.ugolotti at unimib.it>
>     To: David Willock <WillockDJ at cardiff.ac.uk>
>     <mailto:WillockDJ at cardiff.ac.uk>,
>     "ase-users at listserv.fysik.dtu.dk"
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     Subject: Re: [ase-users] trajectory format error during structure
>             optimization
>     Message-ID: <c55d33ce-852e-4815-9044-a66c80d99f0e at unimib.it>
>     <mailto:c55d33ce-852e-4815-9044-a66c80d99f0e at unimib.it>
>     Content-Type: text/plain; charset="utf-8"; Format="flowed"
>
>     Dear David,
>
>
>     thank you for the suggestion, but I don't think that's a mistake I am
>     making. I get such an error message 'when' I read the file/attempt
>     at?
>     getting an image.
>
>
>     Just to clarify, I get the same error message reported above with the
>     two following pieces of code:
>
>
>     1) from ase.io import read
>
>     read('opt.traj',format='trajectory') -->> ERROR
>
>
>     2)? from ase.io.trajectory import TrajectoryReader
>
>
>     TrajectoryReader('opt.traj')[0] -->> ERROR
>
>
>     hence I think the issues should lie in the content of the file. I
>     thought it could have been related to the calculator not cleanly
>     exiting
>     from the optimization step, but I get the same behavior in different
>     conditions.
>
>
>     Aldo
>
>
>     On 08/07/2024 14:28, David Willock wrote:
>     > Dear Aldo,
>     >
>     > From the error message it looks like you are trying to read back
>     the
>     > trajectory file that the optimisers write? The trajectory file is a
>     > list of the structures visited during the optimisation so should be
>     > treated like a list of structures. The ASE site gives details at:
>     >
>     > Trajectory files ? ASE documentation (dtu.dk)
>     >
>     <https://wiki.fysik.dtu.dk/ase/ase/io/trajectory.html
>     <https://wiki.fysik.dtu.dk/ase/ase/io/trajectory.html>>
>     >
>     > Best Wishes
>     > David
>     >
>     >
>     ------------------------------------------------------------------------
>     > *From:*?ase-users <ase-users-bounces at listserv.fysik.dtu.dk>
>     <mailto:ase-users-bounces at listserv.fysik.dtu.dk> on behalf
>     > of Aldo Ugolotti via ase-users <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     > *Sent:*?08 July 2024 13:10
>     > *To:* ase-users at listserv.fysik.dtu.dk
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     > *Subject:*?[ase-users] trajectory format error during structure
>     > optimization
>     > External email to Cardiff University - Take care when
>     replying/opening
>     > attachments or links.
>     > Nid ebost mewnol o Brifysgol Caerdydd yw hwn - Cymerwch ofal wrth
>     > ateb/agor atodiadau neu ddolenni.
>     >
>     >
>     >
>     > Dear users,
>     >
>     > I am optimizing a structure via different optimizers, e.g. FIRE
>     or BFGS,
>     > through a calculator, however I have issues in reading the
>     trajectory
>     > file that is produced.
>     >
>     > When I try to open it, I get the following error messages:
>     >
>     > Traceback (most recent call last):
>     > ?? File "<stdin>", line 1, in <module>
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/formats.py",
>     > line 800, in read
>     > ???? return next(_iread(filename, slice(index, None), format, io,
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/parallel.py",
>     > line 302, in new_generator
>     > ???? for result in generator(*args, **kwargs):
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/formats.py",
>     > line 866, in _iread
>     > ???? for dct in io.read(fd, *args, **kwargs):
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     > line 423, in read_traj
>     > ???? yield trj[i]
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     > line 278, in __getitem__
>     > ???? atoms = read_atoms(b, traj=self)
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     > line 359, in read_atoms
>     > ???? return read_atoms(backend, header, traj, False)
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     > line 379, in read_atoms
>     > ???? atoms = Atoms(positions=b.positions,
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/atoms.py",
>     > line 231, in __init__
>     > ???? self.new_array('positions', positions, float, (3,))
>     > ?? File
>     >
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/atoms.py",
>     > line 491, in new_array
>     > ???? raise ValueError('Array "%s" has wrong length: %d != %d.' %
>     > ValueError: Array "positions" has wrong length: 23 != 20.
>     >
>     > The structure is usually the following (in a POSCAR file):
>     >
>     > Ga O
>     > ? 1.0000000000000000
>     > ????? 3.0437424088662963??? 0.0000000000000000 0.0000000000000000
>     > ????? 0.0000031622422840?? 14.7017269524877570 0.0000000000000000
>     > ????? 0.0000009260717257??? 3.4260834604639068 4.7082612932516961
>     > ? Ga? O
>     > ??? 8? 12
>     > Cartesian
>     > ?? 1.5218723357039710 15.8188718574327893? 2.9079613676911555
>     > ?? 0.0000059327733076 13.1052255051097770? 2.8745980271043003
>     > ? -0.0000107921034274 14.7011495642250427? 0.0085871970445676
>     > ?? 1.5219166606336012 10.7968514552615158? 1.0658204805351676
>     > ?? 3.0437429809987315? 8.4679781419058902? 2.9078954397593910
>     > ?? 1.5218700428854757? 5.7544245018196456? 2.8745176343712169
>     > ?? 1.5218699118892460? 7.3501954535310761? 0.0085254000378572
>     > ?? 3.0437414219421695? 3.4459684229877086? 1.0657976752349458
>     > ?? 0.0000120138472444? 9.9397499435454684? 1.6461898751266788
>     > ?? 1.5218574348726146? 4.2809758546542236? 4.1343011562496468
>     > ?? 3.0437402313938988 14.8510944838742400? 1.8739821734909685
>     > ?? 1.5218703192113834 14.0724457821694671? 3.9088746953136773
>     > ?? 1.5218709568204642 12.4588634753633229? 1.8487030038014953
>     > ?? 3.0437437766782129 16.4641054642267406? 3.9360811195554040
>     > ?? 1.5218728276782361? 2.5889021769267080? 1.6461839979364055
>     > ?? 3.0437389902045822 11.6318087791170388? 4.1343355926457086
>     > ?? 1.5218694913323356? 7.5002250144759159? 1.8739212272855050
>     > ?? 3.0437401536740056? 6.7215584472524945? 3.9088410244254468
>     > ?? 3.0437392898354014? 5.1079805611873921? 1.8486885018616095
>     > ?? 1.5218736571575349? 9.1131861654179929? 3.9359949123592188
>     >
>     >
>     > Can anyone give me an hint about solving this issue?
>     >
>     > Thank you in advance,
>     >
>     > --
>     > Aldo Ugolotti, Ph.D.
>     >
>     > Post-doc fellow
>     > Materials Science Dept. U5,
>     > Universit? degli Studi di Milano-Bicocca
>     > via Cozzi 55,
>     > 20125 Milano (MI)
>     > Italy
>     > e-mail: aldo.ugolotti at unimib.it
>     >
>     > _______________________________________________
>     > ase-users mailing list
>     > ase-users at listserv.fysik.dtu.dk
>     >
>     https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>     <https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users>
>     >
>     <https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>     <https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users>>
>
>     -- 
>     Aldo Ugolotti, Ph.D.
>
>     Post-doc fellow
>     Materials Science Dept. U5,
>     Universit? degli Studi di Milano-Bicocca
>     via Cozzi 55,
>     20125 Milano (MI)
>     Italy
>     e-mail:aldo.ugolotti at unimib.it
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>     ------------------------------
>
>     Message: 2
>     Date: Mon, 8 Jul 2024 13:36:12 +0000
>     From: David Willock <WillockDJ at cardiff.ac.uk>
>     <mailto:WillockDJ at cardiff.ac.uk>
>     To: Aldo Ugolotti <aldo.ugolotti at unimib.it>
>     <mailto:aldo.ugolotti at unimib.it>,
>     "ase-users at listserv.fysik.dtu.dk"
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     Subject: Re: [ase-users] trajectory format error during structure
>             optimization
>     Message-ID:
>     <LO2P265MB5789CA2381C29D3F60D9EEA4ECDA2 at LO2P265MB5789.GBRP265.PROD.OUTLOOK.COM>
>     <mailto:LO2P265MB5789CA2381C29D3F60D9EEA4ECDA2 at LO2P265MB5789.GBRP265.PROD.OUTLOOK.COM>
>
>     Content-Type: text/plain; charset="windows-1252"
>
>     Dear Aldo,
>
>     Does your opt.traj file have any size, i.e. check it is not zero
>     length in case nothing has been written.
>
>     We would usually use the code on the page I sent the link to:
>
>
>     from ase.io.trajectory import Trajectory
>     traj = Trajectory('example.traj')
>     atoms = traj[-1]
>
>     It is difficult to look at this more unless you share the opt.traj
>     file.
>
>     Best Wishes
>     David
>
>     ________________________________
>     From: Aldo Ugolotti <aldo.ugolotti at unimib.it>
>     <mailto:aldo.ugolotti at unimib.it>
>     Sent: 08 July 2024 13:40
>     To: David Willock <WillockDJ at cardiff.ac.uk>
>     <mailto:WillockDJ at cardiff.ac.uk>; ase-users at listserv.fysik.dtu.dk
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     Subject: Re: [ase-users] trajectory format error during structure
>     optimization
>
>
>     Dear David,
>
>
>     thank you for the suggestion, but I don't think that's a mistake I
>     am making. I get such an error message 'when' I read the
>     file/attempt at  getting an image.
>
>
>     Just to clarify, I get the same error message reported above with
>     the two following pieces of code:
>
>
>     1) from ase.io import read
>
>     read('opt.traj',format='trajectory') -->> ERROR
>
>
>     2)  from ase.io.trajectory import TrajectoryReader
>
>
>     TrajectoryReader('opt.traj')[0] -->> ERROR
>
>
>     hence I think the issues should lie in the content of the file. I
>     thought it could have been related to the calculator not cleanly
>     exiting from the optimization step, but I get the same behavior in
>     different conditions.
>
>
>
>     Aldo
>
>
>     On 08/07/2024 14:28, David Willock wrote:
>     Dear Aldo,
>
>     >From the error message it looks like you are trying to read back
>     the trajectory file that the optimisers write? The trajectory file
>     is a list of the structures visited during the optimisation so
>     should be treated like a list of structures. The ASE site gives
>     details at:
>
>     Trajectory files ? ASE documentation
>     (dtu.dk)<https://wiki.fysik.dtu.dk/ase/ase/io/trajectory.html>
>     <https://wiki.fysik.dtu.dk/ase/ase/io/trajectory.html>
>
>     Best Wishes
>     David
>
>     ________________________________
>     From: ase-users <ase-users-bounces at listserv.fysik.dtu.dk>
>     <mailto:ase-users-bounces at listserv.fysik.dtu.dk><mailto:ase-users-bounces at listserv.fysik.dtu.dk>
>     <mailto:ase-users-bounces at listserv.fysik.dtu.dk> on behalf of Aldo
>     Ugolotti via ase-users <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk><mailto:ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     Sent: 08 July 2024 13:10
>     To:
>     ase-users at listserv.fysik.dtu.dk<mailto:ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     <ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk><mailto:ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     Subject: [ase-users] trajectory format error during structure
>     optimization
>
>     External email to Cardiff University - Take care when
>     replying/opening attachments or links.
>     Nid ebost mewnol o Brifysgol Caerdydd yw hwn - Cymerwch ofal wrth
>     ateb/agor atodiadau neu ddolenni.
>
>
>
>     Dear users,
>
>     I am optimizing a structure via different optimizers, e.g. FIRE or
>     BFGS,
>     through a calculator, however I have issues in reading the trajectory
>     file that is produced.
>
>     When I try to open it, I get the following error messages:
>
>     Traceback (most recent call last):
>        File "<stdin>", line 1, in <module>
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/formats.py",
>     line 800, in read
>          return next(_iread(filename, slice(index, None), format, io,
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/parallel.py",
>     line 302, in new_generator
>          for result in generator(*args, **kwargs):
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/formats.py",
>     line 866, in _iread
>          for dct in io.read(fd, *args, **kwargs):
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     line 423, in read_traj
>          yield trj[i]
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     line 278, in __getitem__
>          atoms = read_atoms(b, traj=self)
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     line 359, in read_atoms
>          return read_atoms(backend, header, traj, False)
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/io/trajectory.py",
>     line 379, in read_atoms
>          atoms = Atoms(positions=b.positions,
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/atoms.py",
>     line 231, in __init__
>          self.new_array('positions', positions, float, (3,))
>        File
>     "/home_most1/software/python_virtual_env/enviro_01/lib/python3.10/site-packages/ase/atoms.py",
>     line 491, in new_array
>          raise ValueError('Array "%s" has wrong length: %d != %d.' %
>     ValueError: Array "positions" has wrong length: 23 != 20.
>
>     The structure is usually the following (in a POSCAR file):
>
>     Ga O
>       1.0000000000000000
>           3.0437424088662963    0.0000000000000000 0.0000000000000000
>           0.0000031622422840   14.7017269524877570 0.0000000000000000
>           0.0000009260717257    3.4260834604639068 4.7082612932516961
>       Ga  O
>         8  12
>     Cartesian
>        1.5218723357039710 15.8188718574327893 2.9079613676911555
>        0.0000059327733076 13.1052255051097770 2.8745980271043003
>       -0.0000107921034274 14.7011495642250427 0.0085871970445676
>        1.5219166606336012 10.7968514552615158 1.0658204805351676
>        3.0437429809987315  8.4679781419058902 2.9078954397593910
>        1.5218700428854757  5.7544245018196456 2.8745176343712169
>        1.5218699118892460  7.3501954535310761 0.0085254000378572
>        3.0437414219421695  3.4459684229877086 1.0657976752349458
>        0.0000120138472444  9.9397499435454684 1.6461898751266788
>        1.5218574348726146  4.2809758546542236 4.1343011562496468
>        3.0437402313938988 14.8510944838742400 1.8739821734909685
>        1.5218703192113834 14.0724457821694671 3.9088746953136773
>        1.5218709568204642 12.4588634753633229 1.8487030038014953
>        3.0437437766782129 16.4641054642267406 3.9360811195554040
>        1.5218728276782361  2.5889021769267080 1.6461839979364055
>        3.0437389902045822 11.6318087791170388 4.1343355926457086
>        1.5218694913323356  7.5002250144759159 1.8739212272855050
>        3.0437401536740056  6.7215584472524945 3.9088410244254468
>        3.0437392898354014  5.1079805611873921 1.8486885018616095
>        1.5218736571575349  9.1131861654179929 3.9359949123592188
>
>
>     Can anyone give me an hint about solving this issue?
>
>     Thank you in advance,
>
>     --
>     Aldo Ugolotti, Ph.D.
>
>     Post-doc fellow
>     Materials Science Dept. U5,
>     Universit? degli Studi di Milano-Bicocca
>     via Cozzi 55,
>     20125 Milano (MI)
>     Italy
>     e-mail: aldo.ugolotti at unimib.it<mailto:aldo.ugolotti at unimib.it>
>     <mailto:aldo.ugolotti at unimib.it>
>
>     _______________________________________________
>     ase-users mailing list
>     ase-users at listserv.fysik.dtu.dk<mailto:ase-users at listserv.fysik.dtu.dk>
>     <mailto:ase-users at listserv.fysik.dtu.dk>
>     https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users<https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users>
>     <https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users>
>
>     --
>     Aldo Ugolotti, Ph.D.
>
>     Post-doc fellow
>     Materials Science Dept. U5,
>     Universit? degli Studi di Milano-Bicocca
>     via Cozzi 55,
>     20125 Milano (MI)
>     Italy
>     e-mail: aldo.ugolotti at unimib.it<mailto:aldo.ugolotti at unimib.it>
>     <mailto:aldo.ugolotti at unimib.it>
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>
>     ------------------------------
>
>     Subject: Digest Footer
>
>     _______________________________________________
>     ase-users mailing list
>     ase-users at listserv.fysik.dtu.dk
>     https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users
>     <https://listserv.fysik.dtu.dk/mailman/listinfo/ase-users>
>
>
>     ------------------------------
>
>     End of ase-users Digest, Vol 193, Issue 2
>     *****************************************
>
> -- 
> Aldo Ugolotti, Ph.D.
> Post-doc fellow
> Materials Science Dept. U5,
> Università degli Studi di Milano-Bicocca
> via Cozzi 55,
> 20125 Milano (MI)
> Italy
> e-mail:aldo.ugolotti at unimib.it

-- 
Aldo Ugolotti, Ph.D.

Researcher @ Materials Science Dept. U5,
Università degli Studi di Milano-Bicocca
via Cozzi 55, 20125 Milano (MI)
Italy
Office: U5-2123
Phone: +39 02 6448 5171
e-mail:aldo.ugolotti at unimib.it
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