
973 P.2d 79 (1999)
R.J.M., Appellant,
v.
STATE OF ALASKA, DEPARTMENT OF HEALTH AND SOCIAL SERVICES, Appellee.
P.M., Appellant,
v.
State of Alaska, Department of Health and Social Services, Appellee.
No. S-8525.
Supreme Court of Alaska.
January 29, 1999.
*80 John J. Connors and David G. Parry, Birch, Horton, Bittner & Cherot, Fairbanks, for Appellant R.J.M.
Bonnie J. Coghlan, Fairbanks, for Appellant P.M.
Nora King, Assistant Attorney General, Fairbanks, and Bruce M. Botelho, Attorney General, Juneau, for Appellee.
Before MATTHEWS, Chief Justice, COMPTON, EASTAUGH, FABE, and BRYNER, Justices.

OPINION
EASTAUGH, Justice.

I. INTRODUCTION

The superior court found R.J.M. and P.M. unwilling to care for their son J.M. and under the child in need of aid (CINA) statute, terminated their parental rights. Because P.M.'s failure to seek treatment for her mental illness constitutes unwillingness to provide care, we affirm the termination of her parental rights. Because the superior court did not clearly err in finding that R.J.M. was unwilling to care for J.M., we affirm the termination of R.J.M.'s parental rights. We also affirm the trial court's refusal to consider changed circumstances, and reject R.J.M.'s due process claim.

II. FACTS AND PROCEEDINGS

This case is again before us. In R.J.M. v. State, 946 P.2d 855 (Alaska 1997), we ruled that a finding of emotional neglect could not justify termination of parental rights under AS 47.10.010(a)(2)(F).[1] Our opinion described the facts at that time as follows:
R.J.M. and P.M. were married in 1973. In the course of their marriage, they had two children: a daughter, S.M., born in 1980, and a son, J.M., born in 1985. The family lived in Nenana.
P.M. was the primary caretaker of the children, but suffered from mental problems *81 paranoid and delusional thinking that impeded her ability to provide them with proper care. P.M. kept the children out of school because she believed teachers were prying into the family's life and spreading rumors about her. Although P.M. purported to be home schooling the children, she in fact taught them little if anything.
R.J.M. did not object to P.M.'s treatment of the children or intervene in their behalf. An electronics technician at the Clear Air Force Base, he was "an absent parent" who "saw little of his children and provided little for them other than earning an income."
R.J.M. and P.M. separated in 1990 and entered into an acrimonious divorce action, which culminated in a three-day trial in March 1992. After the separation, P.M. reported that R.J.M. had sexually abused S.M.; as a result of the report, P.M. took custody of S.M. and J.M., and R.J.M.'s contacts with the children were restricted by court order to supervised visits.
On October 22, 1991, during one of the supervised visits, P.M. and R.J.M. became embroiled in an altercation in the children's presence. R.J.M. apparently provoked P.M. until she "totally lost control." P.M. attacked R.J.M. physically, threatened him with a knife, and threw a fork at him; the fork missed R.J.M. but struck J.M. P.M. proceeded to scream obscenities at R.J.M. and the children, ordering S.M. to get out, and telling her to "take a rope and hang yourself in your bedroom."
As a result of this incident, the Division of Family and Youth Services (DFYS) took emergency custody of the children and, two days later, petitioned for temporary CINA custody. The CINA petition described the October 22 altercation and alleged the need to protect J.M. and S.M. from imminent harm arising out of P.M.'s "long and significant history of mental instability," and R.J.M.'s alleged sexual abuse.
Superior Court Judge Mary E. Greene found probable cause to believe that S.M. and J.M. were CINA, and granted temporary custody to the State through December 27, 1991. Some time before then, however, DFYS decided to relinquish custody of the children to R.J.M. P.M.'s accusation of sexual abuse against R.J.M. remained unsubstantiated, and neither child had reported sexual abuse by anyone. "[S]ince [P.M.] was still exhibiting bizarre behaviors which greatly restricted her ability to care for the children, they were returned to the custody of [R.J.M.]."
P.M.'s and R.J.M.'s divorce case was tried before Judge Greene in March 1992; their divorce became final on April 29, 1992. In resolving the issue of custody during the divorce trial, Judge Greene found that P.M. and R.J.M., together, "created an extremely dysfunctional homelife for the children." Nevertheless, the judge also found that the children were generally "happy, healthy, and apparently well-adjusted." Rejecting as "totally unfounded" P.M.'s claims that R.J.M. had sexually abused the children, the judge awarded legal and physical custody to R.J.M., noting that "[P.M.'s] mental problems make it impossible for her to provide good care for the children in meeting all of their needs."
Judge Greene granted P.M. visitation rights, but required that her visits be supervised by a neutral third party "until such time as [P.M.] obtains treatment which will allow her to control her behavior." Judge Greene also ordered "a program of regular counseling" for R.J.M., S.M., and J.M.
S.M. and J.M. remained in R.J.M.'s care from December 1991 until July 1993. During this time, R.J.M. continued to be "an absent parent," hiring a series of nannies to care for the children. On July 14, 1993, the third of these nannies, Nyakerario Omete Brown, who had become romantically involved with R.J.M., reported that she suspected R.J.M. of sexually abusing S.M. Upon receiving Brown's report of sexual abuse, DFYS took emergency custody of the children. The Alaska State Troopers interviewed S.M. the next day (an interview that Judge Greene would later find "seriously flawed"), and S.M. confirmed Brown's report, telling the troopers "that *82 her father had been sexually abusing her over a period of time."
Based on the report of S.M.'s sexual abuse, DFYS filed a CINA petition for temporary custody on July 17, 1993. In August, the initial petition was replaced by a petition reiterating the sexual abuse allegations, noting that S.M. "refuse[d] to return to her father's care," and asserting that S.M.'s abuse in turn "created an unhealthy emotional climate for [J.M.]." The petition went on to state that P.M. was unable to care for the children due to her mental instability. Accordingly, the petition asserted that "[n]either parent is now able to provide for the emotional, mental and social needs of either child."
A month after the children were taken into emergency custody, DFYS psychologist Marti Cranor performed psychological evaluations on them. Cranor reported that J.M. was "undersocialized" and that S.M. had poor socialization skills. Cranor found J.M. to be "an emotionally disturbed boy who struggles with significant feelings of anxiety and depression. He is an unhappy boy whose needs for dependency and protection are not being met." Cranor felt that J.M.'s depression might turn to attempts at suicide. Cranor found S.M. to be "a highly anxious, insecure, and depressed young lady who feels inadequate and inferior"; Cranor also noted that S.M. was "overly concerned with sexual matters," was "at risk for promiscuous behavior," and had "strong needs for support, structure, nurturance, and dependency which are not currently being met."
S.M. and J.M. were initially placed in a foster home in Nenana; at the end of October, DFYS moved them to a foster home in Fairbanks in order to facilitate visitation with P.M. (who lived there) and to give them easier access to counseling.
On October 25, 1993, R.J.M. stipulated, without admitting to any criminal act, that S.M. and J.M. were CINA and that their best interests would be served by committing them to State custody for a period not to exceed two years. As part of the stipulation, R.J.M. agreed to participate in a sexual offender evaluation, and DFYS agreed not to make the results of the evaluation available for criminal prosecution.
The superior court accepted R.J.M.'s stipulation. After a hearing concerning P.M.'s situation, Judge Greene noted that P.M. had failed to follow through on the treatment recommendations made in the divorce action; the judge found P.M. incapable of caring for her children due to her mental problems and concluded that she would remain incapable "until she learns controls on her behavior and develops an understanding of how her behavior impacts the children." The court thus left the children in foster placement.
Beginning in December 1993, S.M. and J.M. were taken out of foster care to spend a five-week visit with P.M. By the end of the visit, J.M. was anxious to go back to Nenana, but S.M. adamantly opposed leaving P.M. DFYS remained convinced, however, that P.M.'s mental problems prevented her from being a viable long-term custodian. The children's therapist recommended that they be given a permanent placement, preferably in Nenana.
Meanwhile, S.M. had recanted her statement to the Alaska State Troopers concerning R.J.M.'s acts of sexual abuse; R.J.M. had been seen by a specialist in the assessment of sexual offenders, who had concluded that R.J.M. did not fit the profile of a pedophile. Having no access to the troopers' criminal investigation files and having never been given the details of Nyakerario Omete Brown's initial report of sexual abuse, DFYS found itself unable to confirm that R.J.M. had sexually abused S.M. Under these circumstances, in mid-January 1994, DFYS reluctantly decided to return the children to R.J.M.
On the day set for return of custody, however, R.J.M., accompanied by Nyakerario Omete Brown, appeared at the DFYS office and notified the children's case worker that "it would not be in the children's best interest to return home that day to him." R.J.M. gave no further explanation. At a follow-up meeting the next week, however, R.J.M. said he would be *83 willing to take the children back at some unspecified future time; he explained that Brown would no longer be living at his house, so he needed to make alternative child-care arrangements.
DFYS took R.J.M.'s behavior as a sign that his children "weren't as important as what was going on in his personal life." At a deposition of Nyakerario Omete Brown conducted in February 1994, DFYS heard for the first time the specifics of Brown's sexual abuse allegations. Furthermore, S.M. seemed "extremely upset" at the prospect of being returned to her father. Accordingly, DFYS reconsidered its options and decided against returning custody to R.J.M.
After again placing the children in foster homes, DFYS decided upon a permanent guardianship arrangement as "the most appropriate goal for the children." S.M. eventually found placement with a family in Seward; J.M.'s Fairbanks foster family volunteered to become his permanent guardians. On December 30, 1994, the court adopted a DFYS case plan recommending permanent guardianships. The following month, DFYS petitioned for appointment of guardians; trial was set for May 1995.
R.J.M. and P.M. actively resisted the State's proposed guardianship arrangements. So actively, in fact, that both sets of prospective guardians felt threatened by R.J.M.'s and P.M.'s actions and began to fear that their efforts to prevent the guardianships might persist and escalate. Both prospective guardian families became reluctant to proceed with the guardianships under these circumstances.
DFYS decided against searching for new guardians: but for the coercive atmosphere created by R.J.M. and P.M., the current placements seemed to be working out well for both children; moreover, altering custody to new guardian candidates might prove futile, since they, too, might be readily threatened and intimidated.
Given R.J.M.'s and P.M.'s history of disruptive parental conduct and the "prospect ... of ongoing embattlement," DFYS concluded that the proposed guardianships were no longer a viable option and that termination of parental rights offered the only realistic chance of preserving the children's current placements. On May 11, 1995, the agency petitioned to terminate R.J.M.'s and P.M.'s parental rights; several days later, the agency moved to dismiss the previously filed guardianship action.[2]
The superior court, in light of the preceding facts, found the children to be CINA under AS 47.10.010(a)(2)(F),[3] which allows state custody of children suffering "substantial physical abuse or neglect."[4] The superior court did not find the children to have been physically neglected. Rather, it read "physical" as modifying only the word "abuse," and held the phrase to include emotional as well as physical neglect.[5] Accordingly, it terminated parental rights over J.M.[6] Because S.M. was already fifteen years old at the time of trial, the superior court denied termination of parental rights over her, but granted CINA custody to the state.[7]
P.M. and R.J.M. appealed the ruling as it related to J.M.[8] We held that the provision cited by the superior court covers only physicaland not emotionalneglect.[9] We did not, however, dismiss the CINA proceeding in its entirety.
*84 Alaska Statute 47.10.010(a)(2)(A)[10] allows CINA jurisdiction if no available person is "caring or willing to provide care" for the child.[11] The superior court had reluctantly held subsection (a)(2)(A) inapplicable because both parents had expressed a willingness to care for their children.[12] While R.J.M.'s first appeal was pending, however, we issued O.R. v. State, 932 P.2d 1303 (Alaska 1997). We there held that mere words are not enough to show willingness to care for one's children in the CINA context:
[W]e interpret subsection (A) to mean that a determination that a parent physically abandoned a child may also support a finding that the parent is not willing to provide care for that child. Indeed, we believe that in many cases the abandonment of a child demonstrates more clearly than testimony the parent's unwillingness to provide care. Thus, ... parents cannot defeat a court's finding of abandonment simply by stating that they are willing to care for a child. Rather, a court ... must look to objective conduct in deter-mining whether a parent is willing to provide care.[13]
In light of O.R., we remanded R.J.M. to the superior court for a determination of whether R.J.M. and P.M. were objectively willing to provide care for J.M. irrespective of their stated willingness.[14]
The superior court found on remand that neither parent was willing to care for J.M. Applying AS 47.10.010(a)(2)(A) and .080(c)(3), the court terminated their parental rights. R.J.M. and P.M. appeal.

III. DISCUSSION


A. Standard of Review

In a CINA case, we will overturn the superior court's finding of facts if they are clearly erroneous.[15] Findings are clearly erroneous if a review of the entire record leaves us with a definite and firm conviction that a mistake has been made.[16]
We apply our independent judgment in reviewing questions of statutory interpretation.[17] Whether the trial court's findings comport with the requirements of the CINA statutes and rules is a question of law which we review de novo.[18]
The adequacy of the notice afforded a litigant in child custody proceedings is a due process issue which is a question of law.[19] We review due process issues de novo.[20]

B. Did the Superior Court Err in Finding P.M. Unwilling to Care for Her Son?

As noted above, AS 47.10.010(a)(2)(A) provides that a court can find a minor a child in need of aid if there is no available person "caring or willing to provide care" for the child. Care in this context means providing *85 "for the physical, emotional, mental, and social needs of the child."[21]
The superior court found on remand that P.M. was unwilling to care for J.M. It stated its rationale:
[P.M.] has long had significant mental health issues which have interfered with her meeting the needs of her children. Without assistance in dealing with her issues, she is unable to provide care. The court finds that a parent objectively willing to provide care would be willing to address the condition which precludes the adequate provision of care. [P.M.] has never been willing to do so. Most of her contacts with mental health professionals have been designed to prove she has no mental health issues.
Moreover, the court cited P.M.'s failure to fully exercise her visitation rights to support its conclusion:
Other actions objectively show [P.M.]'s unwillingness to provide care for [J.M.]. [P.M.] did not consistently visit [J.M.] as much as she was entitled to do. She missed visits; she came late for visits; and she left early during visits. When she did visit, she often put [J.M.] on the spot with inappropriate comments. [P.M.] is not willing to meet [J.M.]'s needs; she has her own agenda and meets her own needs.
The state follows the superior court's reasoning, arguing that P.M. demonstrated her unwillingness to care principally through her unwillingness to seek treatment.
P.M. claims that the state's case against her is based on questions of ability and not willingness. To this end, she argues that her words and actions demonstrate her willingness to care for her children. Moreover, P.M. argues that the superior court conceded she could not be treated. This, she argues, makes her unwillingness to undergo treatment immaterial to her willingness to care for J.M.
But Judge Greene's rulings, both initially and on remand, indicate that the court had concluded that P.M. was treatable. Judge Greene stated in her first ruling:
Instead of doing something about her problems, [P.M.] has consistently denied that she has any and has run from doctor to doctor looking for people to say that she's completely healthy. Her lack of insight makes treatment virtually impossible.
And on remand, she found that
a parent objectively willing to provide care would be willing to address the condition which precludes the adequate provision of care. [P.M.] had never been willing to do so. Most of her contacts with mental health professionals have been designed to prove she has no mental health issues.
P.M. saw a set of psychologists for brief visits, but apparently never entered into any consistent or continuing form of therapy. Her failure to do so directly contravened the advice of at least two of her doctors. Furthermore, P.M. was on notice that improvement of her mental condition was a condition of her continued parental rights. We therefore hold that P.M.'s refusal to pursue psychological help in a genuine, constructive, and committed fashion is evidence of her unwillingness to care for her son. The superior court did not err by finding that P.M. was unwilling to provide care for J.M. within the meaning of AS 47.10.010(a)(2)(A).

C. Did the Superior Court Err in Finding R.J.M. Unwilling to Care for His Son?

On remand, the superior court also found R.J.M. unwilling to care for J.M. The court found that R.J.M. demonstrated his unwillingness through his absenteeism before and after the divorce, his emotional neglect of his son, his refusal to accept physical custody of J.M. in January 1994, his involvement of J.M. in his conflicts with P.M. and the state, and his refusal "to surrender any ground for his son's benefit."
R.J.M. argues that he has shown his willingness to care by repeated efforts to work within the system to obtain custody of J.M., and he cites testimony to support this claim. R.J.M. further argues that he has devoted considerable time and energy to developing a parenting plan, which he argues is proof that *86 he is willing to care for J.M. He explains his reluctance to accept custody in January 1994 as a temporary move to put off custody until he could arrange for a new nanny.[22]
The state argues that R.J.M.'s attempts to participate in treatment and services to improve his parenting were "superficial" and used "largely as ammunition in the legal process rather than vehicles for true change or growth."
We note the potential problems inherent in allowing termination of parental rights for emotional neglect alone. Emotional neglect defies easy characterization; one person's emotional neglect may be, after all, another person's reserve or shyness. In this case, however, there is evidence of more than simple coldness. Among the most significant conduct providing evidence on the issue of R.J.M.'s willingness to care for J.M. is the evidence that R.J.M. refused to accept custody of J.M. in January 1994.[23] We also note that R.J.M. stipulated in 1993 to CINA jurisdiction.[24]
It was not clearly erroneous for the superior court to interpret these objective acts, combined with R.J.M.'s other behavior, as proof that R.J.M. was unwilling to care for J.M.

D. Did the Superior Court Err in Refusing to Consider Evidence of Superseding Conditions During the Two Years between the Original Trial and Its Consideration of the Case on Remand?

On remand, the superior court considered only the factual information that had been available to it at the trial in 1995-96. R.J.M. argues that any change in conditions over the two years since that trial were relevant to J.M.'s best interests, and that the court erred in not considering them.[25] The state argues that the parents' willingness to care for J.M. was the only issue on remand, and that the superior court was under no obligation to reopen the remainder of the case at trial.
We have held that a trial court "has no authority to deviate from a specific mandate of the supreme court but may take actions not inconsistent with [the supreme court's] decision."[26] We have also held that
[o]rdinarily, a remand for additional findings does not obligate the trial court to hear new evidence. We will reverse a trial court's refusal to receive new evidence on remand only when the refusal constitutes an abuse of discretion, unless we have expressly called for a new trial or evidentiary hearing.[27]
In this case, we remanded to the superior court "to allow the trial court to reconsider, in light of O.R., its finding on the issue of willingness to provide care."[28] We did not expressly call for a new trial or evidentiary hearing.
Although the superior court could have considered changed circumstances, it did not abuse its discretion in not doing so. For this reason, we affirm the superior court's refusal to consider any events occurring during the period between the trial and adjudication on remand.

E. Is AS 47.10.010(a)(2)(A) So Vague and Ambiguous that It Violates R.J.M.'s Due Process Rights?

R.J.M. asserts that AS 47.10.010(a)(2)(A) is unconstitutionally vague. He argues that allowing the state to remove a child if the *87 parent "lack[s] empathy" or fails to satisfy a "subjective" standard of willingness to care would deprive the parent of due process.
The words of the United States Supreme Court on vagueness and due process in the criminal law context are instructive here:
Many statutes will have some inherent vagueness, for "[i]n most English words and phrases there lurk uncertainties." Even trained lawyers may find it necessary to consult legal dictionaries, treatises, and judicial opinions before they may say with any certainty what some statutes may compel or forbid. All the Due Process Clause requires is that the law give sufficient warning that men may conduct themselves so as to avoid that which is forbidden.[29]
More directly, we have stated that a statute can be unconstitutionally vague for any of three reasons: (1) it chills First Amendment speech; (2) it fails to give adequate notice of prohibited conduct; and (3) its imprecision "encourages arbitrary enforcement."[30] R.J.M. argues that AS 47.10.010(a)(2)(A) violates the second and third prongs of this vagueness test because the statute provides inadequate notice of what conduct is prohibited and encourages arbitrary enforcement.
R.J.M. cannot prevail on his claim that the statute impermissibly encourages arbitrary enforcement, because he has provided no evidence that the state has arbitrarily enforced this statute. We have held that "we will not invalidate a statute on vagueness grounds absent evidence of a history of arbitrary or capricious enforcement."[31] Neither can R.J.M. prevail on his claim that the statute gives inadequate notice of prohibited conduct. Alaska Statute 47.10.010(a)(2)(A) limits intervention to cases in which the state can prove an ongoing, objectively demonstrated failure to provide basic parental care that reflects unwillingness to serve as a parent. It provides sufficient notice of the grounds for CINA jurisdiction. Accordingly, we reject R.J.M.'s claim that the statute is unconstitutionally vague.

IV. CONCLUSION

The superior court did not err in finding that neither parent was willing to care for J.M. The judgment is AFFIRMED.
NOTES
[1]  See R.J.M. v. State, 946 P.2d 855, 867 (Alaska 1997).
[2]  R.J.M., 946 P.2d at 857-60 (citations omitted).
[3]  Now AS 47.10.010(a)(6). At the time of trial in this case, CINA status was defined in subsections (a)(2)(A)-(F) of AS 47.10.010. The legislature later repealed subsection (a)(1) of the statute; the provisions of subsections (a)(2)(A)-(F) were retained verbatim but were renumbered as AS 47.10.010(a)(1)-(6). AS 42.10.010(a)(6) is thus the current counterpart of former AS 47.10.010(a)(2)(F). We use the former statutory numbering, which governed here. Cf. R.J.M., 946 P.2d at 857 n. 1.
[4]  See R.J.M., 946 P.2d at 860.
[5]  See id. at 862.
[6]  See id. at 860.
[7]  See id.
[8]  See id.
[9]  See id. at 867.
[10]  Now AS 47.10.010(a)(1).
[11]  The relevant text of the statutesince renumbered but otherwise identical to the older versionthen read:

(a) Proceedings relating to a minor under 18 years of age residing or found in the state are governed by this chapter ... when the court finds the minor
....
(2) to be a child in need of aid as a result of
(A) the child being habitually absent from home or refusing to accept available care, or having no parent, guardian, custodian, or relative caring or willing to provide care, including physical abandonment by (i) both parents, (ii) the surviving parent, or (iii) one parent if the other parent's rights and responsibilities have been terminated under AS 25.13.180(c) or AS 47.10.080 or voluntarily relinquished....
[12]  See R.J.M., 946 P.2d at 867. See also In re S.A., 912 P.2d 1235, 1238-42 (Alaska 1996) (denying CINA status where mother was willing to provide care).
[13]  O.R. v. State, 932 P.2d 1303, 1310 (Alaska 1997).
[14]  See R.J.M., 946 P.2d at 869.
[15]  See In re S.A., 912 P.2d at 1237.
[16]  See id. at 1237.
[17]  See R.R. v. State, 919 P.2d 754, 756 n. 3 (Alaska 1996).
[18]  See E.M. v. State, 959 P.2d 766, 768 (Alaska 1998).
[19]  See Lashbrook v. Lashbrook, 957 P.2d 326, 328 (Alaska 1998).
[20]  See id.
[21]  AS 47.10.990(1).
[22]  R.J.M. also argues that O.R. v. State, 932 P.2d 1303 (Alaska 1997), (and its invalidation of "willingness by declaration only") is inapplicable as precedent, because O.R. involved physical abandonment. But we remanded the case at hand with direct instructions to consider O.R. See R.J.M., 946 P.2d at 869.
[23]  See R.J.M., 946 P.2d at 859.
[24]  See id. at 858.
[25]  R.J.M. has had no contact with his son since December 1995, and he relies on conjecture and DFYS documents to support his contention that the child's circumstances have changed.
[26]  A.M. v. State, 945 P.2d 296, 300-01 (Alaska 1997) (footnote omitted).
[27]  Murray v. Murray, 856 P.2d 463, 466 (Alaska 1993) (footnote omitted).
[28]  R.J.M., 946 P.2d at 869.
[29]  Rose v. Locke, 423 U.S. 48, 49-50, 96 S.Ct. 243, 46 L.Ed.2d 185 (1975) (citations omitted); see also Anderson v. State, 562 P.2d 351, 356 n. 10 (Alaska 1977).
[30]  R.R. v. State, 919 P.2d 754, 758 (Alaska 1996) (citing Summers v. Anchorage, 589 P.2d 863, 866-67 (Alaska 1979)).
[31]  Levshakoff v. State, 565 P.2d 504, 507 (Alaska 1977).
